Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
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
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
The aim of this paper is to investigate the first Hochschild cohomology of admissible algebras which can be regarded as a generalization of basic algebras.For this purpose,the authors study differential operators on a...The aim of this paper is to investigate the first Hochschild cohomology of admissible algebras which can be regarded as a generalization of basic algebras.For this purpose,the authors study differential operators on an admissible algebra.Firstly,differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed.Based on this discussion,the first cohomology with admissible algebras as coefficient modules is characterized,including their dimension formula.Besides,for planar quivers,the fc-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field fc of characteristic 0.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
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.
基金supported by the National Natural Science Foundation of China(Nos.11271318,11171296,11401522,J1210038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20110101110010)the Zhejiang Provincial Natural Science Foundation of China(No.LZ13A010001)
文摘The aim of this paper is to investigate the first Hochschild cohomology of admissible algebras which can be regarded as a generalization of basic algebras.For this purpose,the authors study differential operators on an admissible algebra.Firstly,differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed.Based on this discussion,the first cohomology with admissible algebras as coefficient modules is characterized,including their dimension formula.Besides,for planar quivers,the fc-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field fc of characteristic 0.
