In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are ...Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.展开更多
In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the inva...In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.展开更多
Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the m...Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar展开更多
With the help of Bose operator identities and entangled state representation and based on our previous work.[Phys. Lett. A 325 （2004） 188] we derive some new generalized Bessel equations which also have Bessel funct...With the help of Bose operator identities and entangled state representation and based on our previous work.[Phys. Lett. A 325 （2004） 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.展开更多
In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obta...In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.展开更多
As the dynamic equations of space robots are highly nonlinear,strongly coupled and nonholonomic constrained,the efficiency of current dynamic modeling algorithms is difficult to meet the requirements of real-time simu...As the dynamic equations of space robots are highly nonlinear,strongly coupled and nonholonomic constrained,the efficiency of current dynamic modeling algorithms is difficult to meet the requirements of real-time simulation.This paper combines an efficient spatial operator algebra(SOA)algorithm for base fixed robots with the conservation of linear and angular momentum theory to establish dynamic equations for the free-floating space robot,and analyzes the influence to the base body's position and posture when the manipulator is capturing a target.The recursive Newton-Euler kinematic equations on screw form for the space robot are derived,and the techniques of the sequential filtering and smoothing methods in optimal estimation theory are used to derive an innovation factorization and inverse of the generalized mass matrix which immediately achieve high computational efficiency.The high efficient SOA algorithm is spatially recursive and has a simple math expression and a clear physical understanding,and its computational complexity grows only linearly with the number of degrees of freedom.Finally,a space robot with three degrees of freedom manipulator is simulated in Matematica 6.0.Compared with ADAMS,the simulation reveals that the SOA algorithm is much more efficient to solve the forward and inverse dynamic problems.As a result,the requirements of real-time simulation for dynamics of free-floating space robot are solved and a new analytic modeling system is established for free-floating space robot.展开更多
We investigate modular framed vertex operator algebras over an algebraically closed field F whose characteristic is different from 2 and 7.In particular,the rationality of modular framed vertex operator algebras is es...We investigate modular framed vertex operator algebras over an algebraically closed field F whose characteristic is different from 2 and 7.In particular,the rationality of modular framed vertex operator algebras is established.For a modular code vertex operator algebra,the irreducible modules are constructed and classified.Moreover,a Z[1/2]-form for any framed vertex operator algebra over C is constructed.As a result,one can obtain a modular framed vertex operator algebra from any framed vertex operator algebra over C.展开更多
For a vertex operator algebra V with conformal vector w, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and semi- conformal v...For a vertex operator algebra V with conformal vector w, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and semi- conformal vectors of （V, w）, respectively, and were used to study duality theory of vertex operator algebras via coset constructions. Using these objects attached to （V,w）, we shall understand the structure of the vertex operator algebra （V,w）. At first, we define the set Sc（V,w） of semi-conformal vectors of V, then we prove that Sc（V,w） is an aiYine algebraic variety with a partial ordering and an involution map. Corresponding to each semi-conformal vector, there is a unique maximal semi-conformal vertex operator subalgebra containing it. The properties of these subalgebras are invariants of vertex operator algebras. As an example, we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras. As an application, we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties.展开更多
Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L...Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.展开更多
We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra H4 with some natural conditions. It turns out that the representation theory of H4 is quite different from the theory of represent...We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra H4 with some natural conditions. It turns out that the representation theory of H4 is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra VH4 （e, 0） by the even lattice L. We give the structure of the extension VH4 （e, 0） [L] and its irreducible modules via irreducible representations of VH4（e, 0） viewed as a vertex algebra.展开更多
We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral fu...We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.展开更多
In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on...In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2.展开更多
Let A be a standard operator algebra on a Banach space of dimension 〉 1 and B be an arbitrary algebra over Q the field of rational numbers. Suppose that M ： A → B and M^＊ ： B → A are surjective maps such that {M...Let A be a standard operator algebra on a Banach space of dimension 〉 1 and B be an arbitrary algebra over Q the field of rational numbers. Suppose that M ： A → B and M^＊ ： B → A are surjective maps such that {M（r（aM^＊（x）＋M^＊（x）a））=r（M（a）x＋xM（a））, M^＊（r（M（a）x＋xM（a）））=r（aM^＊（x）＋M^＊（x）a） for all a ∈ A, x ∈ B, where r is a fixed nonzero rational number. Then both M and M^＊ are additive.展开更多
We give an explicit description for a weight three generator of the coset vertex operator algebra C_L_(sln)(l,0)L_(sln)(1,0)(L_(sln)(l+1,0),for n≥2, l≥1. Furthermore, we prove that the nommutant C_L_(sl3)(l,0)L_(sl3...We give an explicit description for a weight three generator of the coset vertex operator algebra C_L_(sln)(l,0)L_(sln)(1,0)(L_(sln)(l+1,0),for n≥2, l≥1. Furthermore, we prove that the nommutant C_L_(sl3)(l,0)L_(sl3)(1,0)(L_(sl3)(l+1,0)) is isomorphic to the W-algebra W_(-3+(l+3)/(l+4))(sl_3), which confirms the conjecture for the sl_3 case that C_L_g(l,0)L_g(1,0)(L_g(l + 1,0)) is isomorphic to W_(-h+(l+h)/(l+h+1))(g) for simaly-laced Lie algebras g with its Coxeter number h for a positive integer l.展开更多
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its...In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.展开更多
We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces.
Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B（X）. A map Ф ： A→A is said to be strong 3-commutativity preserving if [Ф（A）, Ф（B）]a = [A, B]3...Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B（X）. A map Ф ： A→A is said to be strong 3-commutativity preserving if [Ф（A）, Ф（B）]a = [A, B]3 for all A, B C .4, where [A, B]3 is the 3-commutator of A, B defined by [A, B]3 = [[[A, B], B], B] with [A, B] = AB - BA. The main result in this paper is shown that, if Ф is a surjective map on A, then Ф is strong 3-commutativity preserving if and only if there exist a functional h ： A→F and a scalar λ∈F with λ^4 = 1 such that Ф（A） = λA ＋ h（A）I for all A ∈A.展开更多
We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules...We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a(not necessarily rigid) braided tensor category of V-modules.We also assume U=ComA(V).Under these conditions,we construct a braid-reversed tensor equivalence τ:u_(A)→v_(A),where u_(A)is the semisimple category of U-modules with simple objects Ui,i∈I,and v_(A)is the category of V-modules whose objects are finite direct sums of Vi.In particular,the V-modules Viare simple and distinct,and v_(A)is a rigid tensor category.As an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p^(-1),p∈Z_(≥2), which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl2-modules.Consequently,the Virasoro vertex operator algebra at central charge 13+6p+6p^(-1)is the PSL_(2)(C)-fixed-point subalgebra of a simple conformal vertex algebra w(-p),analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p^(-1)as the PSL_(2)(C)-fixed-point subalgebra of the triplet algebra W(p).展开更多
For the cyclic group Z_(3)and a positive integer k,we study the representations of the orbifold vertex operator algebra L_(sl_(2))(k,0)^(Z_(3)).All the irreducible modules for L_(sl_(2))(k,0)^(Z_(3))are classified and...For the cyclic group Z_(3)and a positive integer k,we study the representations of the orbifold vertex operator algebra L_(sl_(2))(k,0)^(Z_(3)).All the irreducible modules for L_(sl_(2))(k,0)^(Z_(3))are classified and constructed explicitly.Quantum dimensions and fusion rules for L_(sl_(2))(k,0)^(Z_(3))are completely determined.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
文摘Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.
文摘In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.
基金Supported by the National Natural Science Foundation of China (Grant No.111101250)Innovative Research Team,Department of Applied Mathematics,Shanxi University of Finance & Economics
文摘Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar
基金The project supported by National Natural Science Foundation of China and the President Foundation of the Chinese Academy of Sciences
文摘With the help of Bose operator identities and entangled state representation and based on our previous work.[Phys. Lett. A 325 （2004） 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.
基金supported by the National Natural Science Foundation of China (Nos.12171290,12301152)the Natural Science Foundation of Shanxi Province (No.202203021222018)。
文摘In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.
基金supported by National Natural Science Foundation of China(Grant No.50375071)Commission of Science,Technology and Industry for National Defense Pre-research Foundation of China(Grant No.C4220062501)
文摘As the dynamic equations of space robots are highly nonlinear,strongly coupled and nonholonomic constrained,the efficiency of current dynamic modeling algorithms is difficult to meet the requirements of real-time simulation.This paper combines an efficient spatial operator algebra(SOA)algorithm for base fixed robots with the conservation of linear and angular momentum theory to establish dynamic equations for the free-floating space robot,and analyzes the influence to the base body's position and posture when the manipulator is capturing a target.The recursive Newton-Euler kinematic equations on screw form for the space robot are derived,and the techniques of the sequential filtering and smoothing methods in optimal estimation theory are used to derive an innovation factorization and inverse of the generalized mass matrix which immediately achieve high computational efficiency.The high efficient SOA algorithm is spatially recursive and has a simple math expression and a clear physical understanding,and its computational complexity grows only linearly with the number of degrees of freedom.Finally,a space robot with three degrees of freedom manipulator is simulated in Matematica 6.0.Compared with ADAMS,the simulation reveals that the SOA algorithm is much more efficient to solve the forward and inverse dynamic problems.As a result,the requirements of real-time simulation for dynamics of free-floating space robot are solved and a new analytic modeling system is established for free-floating space robot.
基金supported by the Simons Foundation(Grant No.634104)Ching Hung Lam was supported by Ministry of Science and Technology(Grant No.104-2115-M-001-004-MY3)supported by National Natural Science Foundation of China(Grant No.12071314)。
文摘We investigate modular framed vertex operator algebras over an algebraically closed field F whose characteristic is different from 2 and 7.In particular,the rationality of modular framed vertex operator algebras is established.For a modular code vertex operator algebra,the irreducible modules are constructed and classified.Moreover,a Z[1/2]-form for any framed vertex operator algebra over C is constructed.As a result,one can obtain a modular framed vertex operator algebra from any framed vertex operator algebra over C.
基金supported by the State Scholarship Fund of China Scholarship Council (Grant No. 201208410122)
文摘For a vertex operator algebra V with conformal vector w, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and semi- conformal vectors of （V, w）, respectively, and were used to study duality theory of vertex operator algebras via coset constructions. Using these objects attached to （V,w）, we shall understand the structure of the vertex operator algebra （V,w）. At first, we define the set Sc（V,w） of semi-conformal vectors of V, then we prove that Sc（V,w） is an aiYine algebraic variety with a partial ordering and an involution map. Corresponding to each semi-conformal vector, there is a unique maximal semi-conformal vertex operator subalgebra containing it. The properties of these subalgebras are invariants of vertex operator algebras. As an example, we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras. As an application, we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties.
文摘Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.
文摘We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra H4 with some natural conditions. It turns out that the representation theory of H4 is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra VH4 （e, 0） by the even lattice L. We give the structure of the extension VH4 （e, 0） [L] and its irreducible modules via irreducible representations of VH4（e, 0） viewed as a vertex algebra.
基金Natural Science Foundation of ChinaGrant for Returned Scholars of Shanxi
文摘We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.
基金National Natural Science Foundation of China (10471025,10771034)National Natural Science Foundation of Fujian Province (S0650009)Foudation of the Education Department of Fujian Provience (JA04170,JB07047)
文摘In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10675086 10971117)the Natural Science Foundation of Shandong Province (Grant No.Y2006A03)
文摘Let A be a standard operator algebra on a Banach space of dimension 〉 1 and B be an arbitrary algebra over Q the field of rational numbers. Suppose that M ： A → B and M^＊ ： B → A are surjective maps such that {M（r（aM^＊（x）＋M^＊（x）a））=r（M（a）x＋xM（a））, M^＊（r（M（a）x＋xM（a）））=r（aM^＊（x）＋M^＊（x）a） for all a ∈ A, x ∈ B, where r is a fixed nonzero rational number. Then both M and M^＊ are additive.
基金supported by Japan Society for the Promotion of Science Grants (Grant Nos. 25287004 and 26610006)National Natural Science Foundation of China (Grant Nos. 11371245 and 11531004)
文摘We give an explicit description for a weight three generator of the coset vertex operator algebra C_L_(sln)(l,0)L_(sln)(1,0)(L_(sln)(l+1,0),for n≥2, l≥1. Furthermore, we prove that the nommutant C_L_(sl3)(l,0)L_(sl3)(1,0)(L_(sl3)(l+1,0)) is isomorphic to the W-algebra W_(-3+(l+3)/(l+4))(sl_3), which confirms the conjecture for the sl_3 case that C_L_g(l,0)L_g(1,0)(L_g(l + 1,0)) is isomorphic to W_(-h+(l+h)/(l+h+1))(g) for simaly-laced Lie algebras g with its Coxeter number h for a positive integer l.
基金supported by National Natural Science Foundation of China(Grant Nos.11101269 and 11431010)
文摘In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10926173 and 10771034)Natural Science Foundation of Fujian Province of China (Grant No. 2009J05002)Foundation of Technology and Development of Fuzhou University (Grant No. 2007-XY-11)
文摘We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces.
基金Supported by Natural Science Foundation of China(Grant No.11671294)
文摘Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B（X）. A map Ф ： A→A is said to be strong 3-commutativity preserving if [Ф（A）, Ф（B）]a = [A, B]3 for all A, B C .4, where [A, B]3 is the 3-commutator of A, B defined by [A, B]3 = [[[A, B], B], B] with [A, B] = AB - BA. The main result in this paper is shown that, if Ф is a surjective map on A, then Ф is strong 3-commutativity preserving if and only if there exist a functional h ： A→F and a scalar λ∈F with λ^4 = 1 such that Ф（A） = λA ＋ h（A）I for all A ∈A.
文摘We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a(not necessarily rigid) braided tensor category of V-modules.We also assume U=ComA(V).Under these conditions,we construct a braid-reversed tensor equivalence τ:u_(A)→v_(A),where u_(A)is the semisimple category of U-modules with simple objects Ui,i∈I,and v_(A)is the category of V-modules whose objects are finite direct sums of Vi.In particular,the V-modules Viare simple and distinct,and v_(A)is a rigid tensor category.As an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p^(-1),p∈Z_(≥2), which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl2-modules.Consequently,the Virasoro vertex operator algebra at central charge 13+6p+6p^(-1)is the PSL_(2)(C)-fixed-point subalgebra of a simple conformal vertex algebra w(-p),analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p^(-1)as the PSL_(2)(C)-fixed-point subalgebra of the triplet algebra W(p).
基金supported by the National Natural Science Foundation of China(Grant No.11771281)the Natural Science Foundation of Shanghai(Grant No.16ZR1417800)。
文摘For the cyclic group Z_(3)and a positive integer k,we study the representations of the orbifold vertex operator algebra L_(sl_(2))(k,0)^(Z_(3)).All the irreducible modules for L_(sl_(2))(k,0)^(Z_(3))are classified and constructed explicitly.Quantum dimensions and fusion rules for L_(sl_(2))(k,0)^(Z_(3))are completely determined.
