On the stable module category of a self-injective algebra期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the stable module category of a self-injective algebra

Authors:	Karin Erdmann Otto Kerner

Institution:	Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom ; Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany

Abstract:	Let $\Lambda$ be a finite-dimensional self-injective algebra. We study the dimensions of spaces of stable homomorphisms between indecomposable $\Lambda$ -modules which belong to Auslander-Reiten components of the form $\mathbf{Z}A_\infty$ or $\mathbf{Z}A_\infty/\langle \tau^k\rangle$ . The results are applied to representations of finite groups over fields of prime characteristic, especially blocks of wild representation type.

Keywords:	Stable category of finite-dimensional self-injective algebras quasi-serial Auslander-Reiten components blocks of wild type endo-trivial modules of $p$-group algebras

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