On the First Hochschild Cohomology of Admissible Algebras  

作　　者：Fang LI Dezhan TAN 

机构地区：[1]Department of Mathematics, Zhejiang University [2]College of Mathematics and Information Science, Shangqiu Normal University

出　　处：《Chinese Annals of Mathematics,Series B》2015年第6期1027-1042,共16页数学年刊（B辑英文版）

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)

摘　　要：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.

关 键 词：QUIVER Admissible algebra Differential operators COHOMOLOGY 

分 类 号：O189.22[理学—数学]