交叉积群代数有限维数问题的一点注记

A Note on the Finitistic Dimension of Crossed Product Group Algebras

设G是一个有限群,k是一个代数闭域且k的特征不整除G的阶.Λ是一个扭kG-模代数,Λ*G是一个交叉积代数.该文证明Λ*G和Λ具有相同的有限维数,且同时满足有限维数猜想定理.

Let G be a finite group,k be an algebraically closed field whose characteristic does not divide the order of G,and Λ be a twisted kG-module algebra such that Λ ＊ G exists as a crossed product algebra.We show that the finitistic dimensions of Λ ＊ G and Λ are same and Λ ＊ G satisfies the finitistic dimension conjecture if and only if Λ does.