Universal Deformation Rings of Modules for Algebras of Dihedral Type of Polynomial Growth

被引：7

作者：

Bleher, Frauke M. ^{[1
]}

Talbott, Shannon N. ^{[2
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Coll Mt St Joseph, Dept Math, Cincinnati, OH 45233 USA

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2014年 / 17卷 / 01期

关键词：

Universal deformation rings; Algebras of dihedral type; Polynomial growth; Stable endomorphism rings;

D O I：

10.1007/s10468-012-9399-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k be an algebraically closed field, and let I > be an algebra of dihedral type of polynomial growth as classified by Erdmann and SkowroA"ski. We describe all finitely generated I >-modules V whose stable endomorphism rings are isomorphic to k and determine their universal deformation rings R(I >, V). We prove that only three isomorphism types occur for R(I >, V): k, k[[t]]/(t (2)) and k[[t]].

引用

页码：289 / 303

页数：15

共 13 条

[1]

Auslander M., 1995, CAMBRIDGE STUDIES AD, V36

[2]

Bleher F.M., 2012, T AM MATH S IN PRESS

[3] Universal deformation rings and Klein four defect groups [J].