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SIMPLE MODULES IN THE AUSLANDER–REITEN QUIVER OF PRINCIPAL BLOCKS WITH ABELIAN DEFECT GROUPS

Part of: Representation theory of groups Representation theory of rings and algebras

Published online by Cambridge University Press:  05 February 2018

SHIGEO KOSHITANI  and
CAROLINE LASSUEUR
SHIGEO KOSHITANI
Affiliation:
Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan email koshitan@math.s.chiba-u.ac.jp
CAROLINE LASSUEUR
Affiliation:
FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany email lassueur@mathematik.uni-kl.de
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Abstract

Given an odd prime $p$, we investigate the position of simple modules in the stable Auslander–Reiten quiver of the principal block of a finite group with noncyclic abelian Sylow $p$-subgroups. In particular, we prove a reduction to finite simple groups. In the case that the characteristic is $3$, we prove that simple modules in the principal block all lie at the end of their components.

MSC classification

Primary: 20C20: Modular representations and characters 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
Type
Article
Information
Nagoya Mathematical Journal , Volume 235 , September 2019 , pp. 58 - 85
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

Supported by the Japan Society for Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C)15K04776, 2015–2018.

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