交叉积群代数模范畴的左部分和右部分(英文)

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.

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

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.