An embedding from a group algebra to a matrix algebra is given in this paper. By using it, a criterion for an invertible element in a group algebra is proven.
Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dyn...Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.展开更多
In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A...In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.展开更多
Let A be a normal class of algebras. In the present paper, we characterize the following four problems for A: for which radical class R, there holds that(1) R(i1∧i2) = R(i1)∧R(i2);(2) R(i1∨i2) = R(i1)∨R(i2);(3) (i...Let A be a normal class of algebras. In the present paper, we characterize the following four problems for A: for which radical class R, there holds that(1) R(i1∧i2) = R(i1)∧R(i2);(2) R(i1∨i2) = R(i1)∨R(i2);(3) (i1∧i2) =i1∧i2;(4) (i1∨i2) = i1∨i2, for arbitrary algebra a∈A and any i1,i2∈La,where j denotes the ideal of a uniquely determined by R(a/j) = j/j?展开更多
We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtain...We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.展开更多
Communication network has communication capacity and connection reliability of the links. They canbe independently defined and can be used separately, and when the reliability of a communication network isanalyzed fro...Communication network has communication capacity and connection reliability of the links. They canbe independently defined and can be used separately, and when the reliability of a communication network isanalyzed from a macroscopical angle of view, it is more objective to express the performance index of a commu-nication network as a whole. The reliability index weighted capacity is just obtained by integrating these two pa-rameters. It is necessary to further study the algorithm to calculate the reliability index of the communicationnetwork with a complicated topologic structure and a whole algebraic algorithm is therefore proposed for calcula-tion of the reliability index weighted capacity of a communication network with a topologic structure. The wholecomputational procedure of the algorithm is illustrated with a typical example.展开更多
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left id...We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.展开更多
We prove an equivariant index theorem on the Euclidean space using a continuous field of C^(*)-algebras.This generalizes the work of Elliott et al.(1996),which is a special case of the algebraic index theorem by Nest ...We prove an equivariant index theorem on the Euclidean space using a continuous field of C^(*)-algebras.This generalizes the work of Elliott et al.(1996),which is a special case of the algebraic index theorem by Nest and Tsygan(1995).Using our formula,we see that the equivariant index of the Bott-Dirac operator on R^(2n)can be explicitly calculated.展开更多
The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triang...The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.展开更多
We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-al...We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.展开更多
In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-inject...In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-injective Λ-modules in terms of their socles.Then we prove that a Λ-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ-module.Furthermore,we show that n-minimal Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.展开更多
In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category....In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of H (ρ) and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.展开更多
Let A be a finitely generated associative algebra over a field of characteristic different from 2.Herstein asked when the Lie algebra[A,A]is finitely generated.Recently,it was shown that for a finitely generated nil a...Let A be a finitely generated associative algebra over a field of characteristic different from 2.Herstein asked when the Lie algebra[A,A]is finitely generated.Recently,it was shown that for a finitely generated nil algebra A all derived powers of A are finitely generated Lie algebras.Let K be the Lie algebra of skew-symmetric elements of an associative algebra with involution.We consider all derived powers of the Lie algebra K and prove that for any finitely generated associative nil algebra with an involution,all derived powers of K are finitely generated Lie algebras.展开更多
Let K be a basic field of characteristic 0, and fi,i=1,…,r, be polynomials in K(x1,…Xn)Consider the system of algebraic equations which defines an algebraic variety V consisting of zeros of the system in an arbitrar...Let K be a basic field of characteristic 0, and fi,i=1,…,r, be polynomials in K(x1,…Xn)Consider the system of algebraic equations which defines an algebraic variety V consisting of zeros of the system in an arbitrary extension field of K. The study of the structure of V or that of the set展开更多
Ⅰ. INTRODUCTION In the theory of stability for difference differential equation and functional differential equation, the null points distribution of the transcendental function det (aij+bije-λτ—δijλ)n×n is...Ⅰ. INTRODUCTION In the theory of stability for difference differential equation and functional differential equation, the null points distribution of the transcendental function det (aij+bije-λτ—δijλ)n×n is a basic problem to be studied so far as we know the transcendental criteria for null points distribution of the polynomial H(λ, e-λ) were given by L. S. Pontriagin. Qin Yuanxun et al. offered the equivalent algebraic criteria. All these are sufficient and necessary conditions. But when n≥2, it is rather difficult to check the conditions of these criteria.展开更多
Suppose that A is an n×n complex matrix. Denote by G(A)the contragradient Lie algebra corresponding to the matrix A. If A is a generalized Cartan matrix, we call G(A) a Kac-Moody Lie algebra.
Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the pers...Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.展开更多
We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self abs...We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self absorbing C^(*)-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_(2)),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(resp.properly infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.展开更多
We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was pre...We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.展开更多
We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-tr...We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.展开更多
文摘An embedding from a group algebra to a matrix algebra is given in this paper. By using it, a criterion for an invertible element in a group algebra is proven.
文摘Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.
基金The National Science Foundation (99A019, 2002X10) of the Education Committee of Hubei Province.
文摘In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.
基金The NSF (2024201051) of Liaoning Education Department.
文摘Let A be a normal class of algebras. In the present paper, we characterize the following four problems for A: for which radical class R, there holds that(1) R(i1∧i2) = R(i1)∧R(i2);(2) R(i1∨i2) = R(i1)∨R(i2);(3) (i1∧i2) =i1∧i2;(4) (i1∨i2) = i1∨i2, for arbitrary algebra a∈A and any i1,i2∈La,where j denotes the ideal of a uniquely determined by R(a/j) = j/j?
基金Supported by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banachthe PAI with project numbers FQM-298 and FQM-336the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with fondos FEDER
文摘We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.
基金Sponsored by the Natural Science Foundation of Harbin Institute of Technology (Weihai) (Grant No. HIT(WH). 2002. 7)
文摘Communication network has communication capacity and connection reliability of the links. They canbe independently defined and can be used separately, and when the reliability of a communication network isanalyzed from a macroscopical angle of view, it is more objective to express the performance index of a commu-nication network as a whole. The reliability index weighted capacity is just obtained by integrating these two pa-rameters. It is necessary to further study the algorithm to calculate the reliability index of the communicationnetwork with a complicated topologic structure and a whole algebraic algorithm is therefore proposed for calcula-tion of the reliability index weighted capacity of a communication network with a topologic structure. The wholecomputational procedure of the algorithm is illustrated with a typical example.
文摘We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.
基金supported by National Natural Science Foundation of China(Grant No.12271165)Shanghai Fundamental Research Project(Grant No.23JC1401900)the Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。
文摘We prove an equivariant index theorem on the Euclidean space using a continuous field of C^(*)-algebras.This generalizes the work of Elliott et al.(1996),which is a special case of the algebraic index theorem by Nest and Tsygan(1995).Using our formula,we see that the equivariant index of the Bott-Dirac operator on R^(2n)can be explicitly calculated.
文摘The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.
基金supported by National Natural Science Foundation of China(Grant Nos.11171109 and 11801177)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.
基金supported by the National Natural Science Foundation of China(11671230,11371165).
文摘In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-injective Λ-modules in terms of their socles.Then we prove that a Λ-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ-module.Furthermore,we show that n-minimal Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.
基金supported in part by NSF of China (Grant No. 10631010)NKBRPC (Grant No. 2006CB805905)
文摘In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of H (ρ) and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.
基金funded by King Abdulaziz University,Deanship of Scientific Research(grant number RG-50-130-39).
文摘Let A be a finitely generated associative algebra over a field of characteristic different from 2.Herstein asked when the Lie algebra[A,A]is finitely generated.Recently,it was shown that for a finitely generated nil algebra A all derived powers of A are finitely generated Lie algebras.Let K be the Lie algebra of skew-symmetric elements of an associative algebra with involution.We consider all derived powers of the Lie algebra K and prove that for any finitely generated associative nil algebra with an involution,all derived powers of K are finitely generated Lie algebras.
文摘Let K be a basic field of characteristic 0, and fi,i=1,…,r, be polynomials in K(x1,…Xn)Consider the system of algebraic equations which defines an algebraic variety V consisting of zeros of the system in an arbitrary extension field of K. The study of the structure of V or that of the set
文摘Ⅰ. INTRODUCTION In the theory of stability for difference differential equation and functional differential equation, the null points distribution of the transcendental function det (aij+bije-λτ—δijλ)n×n is a basic problem to be studied so far as we know the transcendental criteria for null points distribution of the polynomial H(λ, e-λ) were given by L. S. Pontriagin. Qin Yuanxun et al. offered the equivalent algebraic criteria. All these are sufficient and necessary conditions. But when n≥2, it is rather difficult to check the conditions of these criteria.
文摘Suppose that A is an n×n complex matrix. Denote by G(A)the contragradient Lie algebra corresponding to the matrix A. If A is a generalized Cartan matrix, we call G(A) a Kac-Moody Lie algebra.
基金supported by the National Natural Science Foundation of China(Nos.11771143,11831006,11420101001).
文摘Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.
基金supported by the Research Center for Operator Algebras at East China Normal University which is funded by the Science and Technology Commission of Shanghai Municipality (Grant No.13dz2260400)National Natural Science Foundation of China (Grant No.11531003)+1 种基金Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice (Grant No.1361431)the special fund for the Short-Term Training of Graduate Students from East China Normal University。
文摘We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self absorbing C^(*)-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_(2)),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(resp.properly infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.
基金supported by projects MTM 2008-03339 from the Ministerio de Cienica e In,P07-FQM03128FQM0211 from Junta de Andalucía and TEC 2009-13763-C02-02
文摘We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.
基金I+D MEC Projects No.MTM 2005-02541,MTM 2004-03882Junta de Andalucfa Grants FQM 0199,FQM 0194,FQM 1215the PCI Project No.A/4044/05 of the Spanish AECI
文摘We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.
