The Auslander-Reiten quiver of a finite group
The Auslander-Reiten quiver of a finite group
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DOI：
10.1007/bf01173918
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发表时间：
1982-03
影响因子：
0.8
通讯作者：
P. Webb
中科院分区：
文献类型：
--
作者：
P. Webb
在本文中，G将是一个有限群，R将表示特征p>；0的域k，或特征p的有限剩余类域的完备一阶离散赋值环(0)。我们的主要目的是刻画群环RG的Austander-Reiten箭图A(RG)。这是一个有向图，它的顶点是不可分解的RG-模的同构类型(在R=(9，我们只考虑不可分解的RG-格)的情况下)，并且当存在不可约的态射f：M-~N时，存在边M-~N。这些边用一对数字来拟合
Throughout this paper G will be a finite group and R will denote either a field k of characteristic p> 0, or a complete rank one discrete valuation ring (0 with finite residue class field of characteristic p. Our main purpose is to describe the Austander-Reiten quiver A (RG) of the group ring RG. This is the directed graph whose vertices are the isomorphism types of indecomposable RG-mo~ dules (in case R=(9 we consider only indecomposable RG-tattices) and in which there are edges M-~ N whenever there is an irreducible morphism f: M-~ N. These edges come fitted with a pair of numbers