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
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.展开更多
A technique is provided to explicitly describe global dimensions of all An-type finite dimensional k-algebras for k an algebraic closed field. All possible global dimensions of all AN-type finite dimensional algebras ...A technique is provided to explicitly describe global dimensions of all An-type finite dimensional k-algebras for k an algebraic closed field. All possible global dimensions of all AN-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is n - 1, and the minimum is 1 for n 〉 1.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the form of a type of algebraic differential equation with admissible meromorphic solutions and obtain a Malmquist type theorem.
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 ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators ...The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to its quotient algebra as an admissible algebra ave 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 k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k 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 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.
基金Supported by the National Natural Science Foundation of China(Grant No.11371307)
文摘A technique is provided to explicitly describe global dimensions of all An-type finite dimensional k-algebras for k an algebraic closed field. All possible global dimensions of all AN-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is n - 1, and the minimum is 1 for n 〉 1.
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the form of a type of algebraic differential equation with admissible meromorphic solutions and obtain a Malmquist type theorem.
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 ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to its quotient algebra as an admissible algebra ave 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 k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k of characteristic 0.
