Graded Hochschild Cohomology of a Path Algebra with Oriented Cycles

作     者：Fang LI De Zhan TAN 

作者机构：Department of MathematicsZhejiang University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第9期

页      面：1495-1512页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.10871170 and 11171296) the Zhejiang Provincial Natural Science Foundation of China(Grant No.D7080064) 

主　　题：Quiver. genus graded Hochschild cohomology graded Lie algebras oriented cycle 

摘      要：The aim of this paper is to characterize the first graded Hochschild cohomology of a hereditary algebra whose Gabriel quiver is admitted to have oriented cycles. The interesting conclusion we have obtained shows that the standard basis of the first graded Hochschild cohomology depends on the genus of a quiver as a topological object. In this paper, we overcome the limitation of the classical Hochschild cohomology for hereditary algebra where the Gabriel quiver is assumed to be acyclic. As preparation, we first investigate the graded differential operators on a path algebra and the associated graded Lie algebra.