On Connected Components of Skew Group Algebras  

作　　者：Jian Min CHEN Qiang DONG Ya Nan LIN 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第5期799-813,共15页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11871404,11971398 and 12131018)。

摘　　要：Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equivalent to the quotient algebra of path algebra kQGmodulo ideal(ρG).Generally,the quiver QGis not connected.In this paper we develop a method to determine the number of connect components of QG.Meanwhile,we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.

关 键 词：Smash product skew group algebra n-translation algebra path algebra connected component 

分 类 号：O152.1[理学—数学]