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
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.
