Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
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
In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras w...In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie 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
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
Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm...Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.展开更多
In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-...In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.展开更多
The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vecto...The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,which is a finite set consisting of two nontrivial elements.Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras.Moreover,associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,we charaterized twisted Heisenberg-Virasoro vertex operator algebras.This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.展开更多
In this paper,we first introduce the notion of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras and give some characteristics of relative Rota-Baxter operators in terms of Nijenhuis operators and graphs.The...In this paper,we first introduce the notion of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras and give some characteristics of relative Rota-Baxter operators in terms of Nijenhuis operators and graphs.Then,the cohomology theory of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras is proposed.Finally,the deformation of the relative Rota-Baxter operator is explored by applying the cohomological approach.展开更多
In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a ...In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.展开更多
Let K be a field of characteristic p>0 . We prove that the derivative algebra of K[x 1,…,x n] is a proer subring of the ring of differential operators of K[x 1,…,x n] . A concrete example is given to show that th...Let K be a field of characteristic p>0 . We prove that the derivative algebra of K[x 1,…,x n] is a proer subring of the ring of differential operators of K[x 1,…,x n] . A concrete example is given to show that there is a differential operator of order p that does not belong to the derivative algebra. By these results, is follows that the derivative algebra is Morita equivalent to K[x p 1,…,x p n] , and hence its global homological dimension, Krull dimension, K 0 group and some other properties are got.展开更多
In this paper, the continuity of consequence operators is introduced. Relations between consequence operators and their associated information algebras are mainly explored. It is shown that, for any given consequence ...In this paper, the continuity of consequence operators is introduced. Relations between consequence operators and their associated information algebras are mainly explored. It is shown that, for any given consequence operator, the associated information algebra can be directly constructed without any additional conditions.Furthermore, if the consequence operators are continous or compact, then the associated information algebras are continuous or compact.展开更多
A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstra...A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.展开更多
In terms of the exactly nonzero partition,the reducible projection-system and correlation matrices,two characterizations for a rank three operator in a CSL algebra can be completely decomposed are given.
In this paper, a necessary condition for a maximal triangular algebra to be closed is given. A necessary and sufficient condition for a maximal triangular algebra to be strongly reducible is obtained.
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
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
In this paper,we give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra D(2,1;α).Based on these expressions,we construct free field realizations of the currents...In this paper,we give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra D(2,1;α).Based on these expressions,we construct free field realizations of the currents associated with D(2,1;α) at an arbitrary level k.展开更多
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
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.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY231)。
文摘In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie 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.
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.
基金partly supported by Natural Science Foundation of the Xinjiang Uygur Autonomous Region(2013211A001)
文摘Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.
基金The NSF(11047030 and 11771122) of Chinathe Science and Technology Program(152300410061) of Henan Province
文摘In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.
基金supported by The Key Research Project of Institutions of Higher Education in Henan Province,P.R.China(No.17A11003)
文摘The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,which is a finite set consisting of two nontrivial elements.Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras.Moreover,associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,we charaterized twisted Heisenberg-Virasoro vertex operator algebras.This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.
基金Supported by the Foundation of Science and Technology of Guizhou Province(Grant No.[2018]1020)the Guizhou University of Finance and Economics introduced talent research projects(2016)the National Natural Science Foundation of China(Grant No.12161013)。
文摘In this paper,we first introduce the notion of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras and give some characteristics of relative Rota-Baxter operators in terms of Nijenhuis operators and graphs.Then,the cohomology theory of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras is proposed.Finally,the deformation of the relative Rota-Baxter operator is explored by applying the cohomological approach.
基金Supported by National Natural Science Foundation of China under Grant Nos.11471139,11271202,11221091,11425104Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20120031110022National Natural Science Foundation of Jilin Province under Grant No.20140520054JH
文摘In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.
文摘Let K be a field of characteristic p>0 . We prove that the derivative algebra of K[x 1,…,x n] is a proer subring of the ring of differential operators of K[x 1,…,x n] . A concrete example is given to show that there is a differential operator of order p that does not belong to the derivative algebra. By these results, is follows that the derivative algebra is Morita equivalent to K[x p 1,…,x p n] , and hence its global homological dimension, Krull dimension, K 0 group and some other properties are got.
基金The NSF(61702389) of ChinaScientific Research Program Fund(18JK0315) of Shaanxi Provincial Education Department
文摘In this paper, the continuity of consequence operators is introduced. Relations between consequence operators and their associated information algebras are mainly explored. It is shown that, for any given consequence operator, the associated information algebra can be directly constructed without any additional conditions.Furthermore, if the consequence operators are continous or compact, then the associated information algebras are continuous or compact.
文摘A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.
文摘In terms of the exactly nonzero partition,the reducible projection-system and correlation matrices,two characterizations for a rank three operator in a CSL algebra can be completely decomposed are given.
文摘In this paper, a necessary condition for a maximal triangular algebra to be closed is given. A necessary and sufficient condition for a maximal triangular algebra to be strongly reducible is obtained.
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Supported in part by National Natural Science Foundation of China under Grant No. 10971071the Outstanding Youth Fund of Henan Province under Grant No. 0512000100Innovation Fund of Colleges and Universities in Henan Province
文摘In this paper, we construct a new algebra structure 7-twisted atone Lie algebra sl（3,C）[θ] and study its vertex operator representations.
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Support from the National Natural Science Foundation of China under Grant Nos.10931006,10975180,and 11075126the Ministry of Education of China under Grant No.20116101110017Northwest University Graduate Cross-Discipline Fund (10YJC15)
文摘In this paper,we give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra D(2,1;α).Based on these expressions,we construct free field realizations of the currents associated with D(2,1;α) at an arbitrary level k.
