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
In the current work,we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras,and hence of split Lie algebras.In particular,we show that an arbitrary graded...In the current work,we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras,and hence of split Lie algebras.In particular,we show that an arbitrary graded regular BiHom-Lie algebra L can be expressed as L=U+∑_(j)I_(j),where U is a linear subspace in L_(1),1 being the neutral element of the grading group,and any I_(j)a well-described(graded)ideal of L,satisfying[I_(j),I_(k)]=0 if j≠k.Moreover,under some conditions,we characterize the simplicity of L and we show that L is the direct sum of the family of its simple(graded)ideals.The first author was supported by the Centre for Mathematics of the University of Coimbra(UIDB/00324/2020),funded by the Portuguese Government through FCT/MCTES.The second and fourth authors are supported by the PCI of UCA`Teoría de Lie y Teoría de Espacios de Banach'and the PAI with project number FQM298.The second author is also supported by the 2014-2020 ERDF Operational Programme and by the Department of Economy,Knowledge,Business and University of the Regional Government of Andalusia FEDER-UCA18-107643.The third author is supported by Agencia Estatal de Investigación(Spain),grant PID2020-115155GB-I00(European FEDER support included,EU).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
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 Centre for Mathematics of the University of Coimbra(UIDB/00324/2020)funded by the Portuguese Government through FCT/MCTES+2 种基金supported by the PCI of UCA'Teoría de Lie y Teoría de Espacios de Banach'and the PAI with project number FQM298supported by the 2014-2020 ERDF Operational Programme and by the Department of Economy,Knowledge,Business and University of the Regional Government of Andalusia FEDER-UCA18-107643supported by Agencia Estatal de Investigación(Spain),grant PID2020-115155GB-I00(European FEDER support included,EU).
文摘In the current work,we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras,and hence of split Lie algebras.In particular,we show that an arbitrary graded regular BiHom-Lie algebra L can be expressed as L=U+∑_(j)I_(j),where U is a linear subspace in L_(1),1 being the neutral element of the grading group,and any I_(j)a well-described(graded)ideal of L,satisfying[I_(j),I_(k)]=0 if j≠k.Moreover,under some conditions,we characterize the simplicity of L and we show that L is the direct sum of the family of its simple(graded)ideals.The first author was supported by the Centre for Mathematics of the University of Coimbra(UIDB/00324/2020),funded by the Portuguese Government through FCT/MCTES.The second and fourth authors are supported by the PCI of UCA`Teoría de Lie y Teoría de Espacios de Banach'and the PAI with project number FQM298.The second author is also supported by the 2014-2020 ERDF Operational Programme and by the Department of Economy,Knowledge,Business and University of the Regional Government of Andalusia FEDER-UCA18-107643.The third author is supported by Agencia Estatal de Investigación(Spain),grant PID2020-115155GB-I00(European FEDER support included,EU).
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partially supported by NSFC(No.11761017)the Key University Science Research Project of Anhui Province(Nos.KJ2015A294,KJ2014A183,KJ2016A545)+2 种基金the NSF of Chuzhou University(Nos.2014PY08,2015QD01)the Fund of Science and Technology Department of Guizhou Province(No.[2016]1021)the Youth Project for Natural Science Foundation of Guizhou Provincial Department of Education(No.KY[2018]155)
基金Supported by NNSF of China (11801121)NSF of Heilongjiang province(QC2018006)the Fundamental Research Fundation for Universities of Heilongjiang Province(LGYC2018JC002)。
