The aim of this paper is to show that every local 2-cocycle of a von Neumann algebra R with coefficients in S (a unital dual R-bimodule) is a 2-cocycle.
In this paper,we prove that every generalized Jordan derivation associate with a Hochschild 2-cocycle from the algebra of upper triangular matrices to its bimodule is the sum of a generalized derivation and an antider...In this paper,we prove that every generalized Jordan derivation associate with a Hochschild 2-cocycle from the algebra of upper triangular matrices to its bimodule is the sum of a generalized derivation and an antiderivation.展开更多
In this paper, we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus, which are called the Triangular derivation Lie algebra. We give the structure and the central extension of Tri...In this paper, we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus, which are called the Triangular derivation Lie algebra. We give the structure and the central extension of Triangular derivation Lie algebra.展开更多
A simpler definition for a class of 2-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form.Their positive parts turn out to be 2-cocycle deformations of each other under some ...A simpler definition for a class of 2-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form.Their positive parts turn out to be 2-cocycle deformations of each other under some conditions.An operator realization of the positive part is given.展开更多
In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and th...In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.展开更多
In this paper, we give a sufficient condition for double crossproduct X A to be X A for some skew pairing T if X A is a 2-cocycle deformation of X A. Then we give a sufficient and necessary condition for X A to b...In this paper, we give a sufficient condition for double crossproduct X A to be X A for some skew pairing T if X A is a 2-cocycle deformation of X A. Then we give a sufficient and necessary condition for X A to be X A by using natural isomorphism terminology.展开更多
基金the National Natural Science Foundation of China(1 0 0 71 0 4 7)
文摘The aim of this paper is to show that every local 2-cocycle of a von Neumann algebra R with coefficients in S (a unital dual R-bimodule) is a 2-cocycle.
基金Supported by the National Natural Science Foundation of China (Grant No. A010602)
文摘In this paper,we prove that every generalized Jordan derivation associate with a Hochschild 2-cocycle from the algebra of upper triangular matrices to its bimodule is the sum of a generalized derivation and an antiderivation.
基金Supported by the National Natural Science Foundation of China (Grant No. 11171294)the Natural Science Foundation of Heilongjiang Province (Grant No. A201013)the Fund of Heilongjiang Education Committee(Grant No. 11541268)
文摘In this paper, we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus, which are called the Triangular derivation Lie algebra. We give the structure and the central extension of Triangular derivation Lie algebra.
基金the National Natural Science Foundation of China(Grant Nos.10431040,10728102)the TRAPOYT,the FUDP and the Priority Academic Discipline from the MOE of China,the SRSTP from the STCSM,the Shanghai Priority Academic Discipline from the SMEC
文摘A simpler definition for a class of 2-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form.Their positive parts turn out to be 2-cocycle deformations of each other under some conditions.An operator realization of the positive part is given.
基金Supported by National Natural Science Foundation of China(Grant Nos.11431010,11371278 and 11271284)Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)
文摘In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.
文摘In this paper, we give a sufficient condition for double crossproduct X A to be X A for some skew pairing T if X A is a 2-cocycle deformation of X A. Then we give a sufficient and necessary condition for X A to be X A by using natural isomorphism terminology.
