The purpose of this paper is to define Hochschild type homology of Bihomassociative algebras and Chevalley-Eilenberg type homology of Bihom-Lie algebras with non-trivial coefficients in their bimodules respectively.In...The purpose of this paper is to define Hochschild type homology of Bihomassociative algebras and Chevalley-Eilenberg type homology of Bihom-Lie algebras with non-trivial coefficients in their bimodules respectively.In particular,we give their low order homology in detail.展开更多
The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the h...The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.展开更多
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some ...In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.展开更多
We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
A Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps.In this paper,we study representations of Bihom-Lie algebras.In particular,derivations,central extensions,deri...A Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps.In this paper,we study representations of Bihom-Lie algebras.In particular,derivations,central extensions,derivation extensions,the trivial representation and the adjoint representation of Bihom-Lie algebras are studied in detail.展开更多
基金Supported by the National Science Foundation of China(Grant Nos.11047030,11171055).
文摘The purpose of this paper is to define Hochschild type homology of Bihomassociative algebras and Chevalley-Eilenberg type homology of Bihom-Lie algebras with non-trivial coefficients in their bimodules respectively.In particular,we give their low order homology in detail.
基金The Natural Science Foundation of Jiangsu Province(No.BK2012736)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
基金National Natural Science Foundation of China(10271076)
文摘In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
文摘We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
基金Supported by NNSF of China (11801121)NSF of Heilongjiang province(QC2018006)the Fundamental Research Fundation for Universities of Heilongjiang Province(LGYC2018JC002)。
基金Supported by the National Science Foundation of China(Nos.11047030 and 11771122).
文摘A Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps.In this paper,we study representations of Bihom-Lie algebras.In particular,derivations,central extensions,derivation extensions,the trivial representation and the adjoint representation of Bihom-Lie algebras are studied in detail.
