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BLOCKS WITH SMALL-DIMENSIONAL BASIC ALGEBRA

Part of:Representation theory of groupsModules, bimodules and ideals

Published online by Cambridge University Press:  21 September 2020

BENJAMIN SAMBALEOpen the ORCID record for BENJAMIN SAMBALE[Opens in a new window]
BENJAMIN SAMBALE*
Affiliation:
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
*
e-mail: sambale@math.uni-hannover.de
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Abstract

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Linckelmann and Murphy have classified the Morita equivalence classes of p-blocks of finite groups whose basic algebra has dimension at most $12$. We extend their classification to dimension $13$ and $14$. As predicted by Donovan’s conjecture, we obtain only finitely many such Morita equivalence classes.

Keywords

basic block algebraMorita equivalenceDonovan’s conjecture

MSC classification

Primary:20C05: Group rings of finite groups and their modules
Secondary:16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021, pp. 461 - 474
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Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

This work is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).

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