有限交换群在路代数上的分次作用

Graded Actions of Finite Abelian Groups on Path Algebras

主要研究有限交换群在路代数上的分次作用。首先证明对于任意的群在路代数上的作用,群元素诱导的线性变换可分解为分次自同构和幂零线性变换的和。讨论了群作用的平移性质,和共轭不变量。然后将结论用于讨论有限循环群和有限交换群在路代数上的分次作用。

The graded actions of finite abelian groups on path algebras is studied in this paper.For any group action on a path algebra,the linear transformation induced by a group element can be decomposed into the sum of graded automorphism and nilpotent linear transformation.Translation properties of group actions are discussed,and invariants of congruence are determined.The graded actions of finite cyclic groups and finite abelian groups on path algebras are studied.