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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the stable module category of a self-injective algebra


Authors: Karin Erdmann and Otto Kerner
Journal: Trans. Amer. Math. Soc. 352 (2000), 2389-2405
MSC (2000): Primary 18G25; Secondary 16G70, 20C20
DOI: https://doi.org/10.1090/S0002-9947-00-02232-7
Published electronically: February 14, 2000
MathSciNet review: 1487612
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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.


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Additional Information

Karin Erdmann
Affiliation: Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
Email: erdmann@maths.ox.ac.uk

Otto Kerner
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
Email: kerner@cs.uni-duesseldorf.de

DOI: https://doi.org/10.1090/S0002-9947-00-02232-7
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
Received by editor(s): June 4, 1996
Received by editor(s) in revised form: October 2, 1997
Published electronically: February 14, 2000
Article copyright: © Copyright 2000 American Mathematical Society