交叉积群代数模范畴的左部分和右部分(英文)

The Left and Right Parts of the Module Category of Crossed Product Group Algebras

设G是一个有限群,k为一个特征不整除G的阶数的域,∧是一个扭kG-模代数,且∧*_σG(简写为∧*G)是一个交叉积代数.设L_∧(R_∧)为代数∧的模范畴中前缀(后缀)的投射(内射)维数至多为1的所有有限生成的不可分解模.本文主要研究了交叉积代数∧*G的模范畴左(右)部分L_(∧*G)(R_(∧*G))与代数∧的左(右)部分L_∧(R_∧)之间的关系.最后,利用本文得到的结果,考察了代数∧的相关性质在交叉积扩张下在代数∧*G中的保持性.

Let G be a finite group,k be a field with characteristic not dividing the order of G,and A be a twisted kG-module algebra such thatΛ＊_σG orΛ＊ G for short exists as a crossed product algebra.In this paper,we study the relationship between the class L_（Λ＊G）（or R_（Λ＊G））, which consists of all finitely generated indecomposable A ＊ G-modules whose predecessors（or successors） have projective dimension（or injective dimension） at most one,and the classL_Λ（or R_Λ）.Then we study those properties,which rely on the left（or right） part,of A that are preserved under the extension of crossed product group algebra A ＊ G.