Universal deformation rings and self-injective Nakayama algebras |
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Authors: | Frauke M Bleher Daniel J Wackwitz |
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Institution: | 1. Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA;2. Department of Mathematics, University of Wisconsin-Platteville, 435 Gardner Hall, 1 University Plaza, Platteville, WI 53818, USA |
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Abstract: | Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring and we describe explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups. |
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Keywords: | Primary 16G10 secondary 16G20 20C20 |
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