Rank varieties for a class of finite-dimensional local algebras

被引:17
作者
Benson, David J.
Erdmann, Karin
Holloway, Miles
机构
[1] Univ Aberdeen, Kings Coll, Dept Math Sci, Aberdeen AB24 3UE, Scotland
[2] Math Inst, Oxford OX1 3LB, England
关键词
D O I
10.1016/j.jpaa.2007.02.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We develop a rank variety for finite-dimensional modules over a certain class of finite-dimensional local k-algebras, A(q,m)(n). Included in this class are the truncated polynomial algebras k[X1,..., X-m]/(X-i(n)), with k an algebraically closed field and char(k) arbitrary. We prove that these varieties characterise projectivity of modules (Dade's lemma) and examine the implications for the tree class of the stable Auslander-Reiten quiver. We also extend our rank varieties to infinitely generated modules and verify Dade's lemma in this context. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:497 / 510
页数:14
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