Graded Hochschild Cohomology of a Path Algebra with Oriented Cycles  

作　　者：Fang LI De Zhan TAN 

机构地区：[1]Department of Mathematics,Zhejiang University

出　　处：《Acta Mathematica Sinica,English Series》2014年第9期1495-1512,共18页数学学报（英文版）

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)

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.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.

关 键 词：Quiver. genus graded Hochschild cohomology graded Lie algebras oriented cycle 

分 类 号：O189.22[理学—数学]