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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Almost split sequences for group algebras of finite representation type


Author: Idun Reiten
Journal: Trans. Amer. Math. Soc. 233 (1977), 125-136
MSC: Primary 16A26; Secondary 20C05
MathSciNet review: 0573041
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Abstract: Let k be an algebraically closed field of characteristic p and G a finite group such that p divides the order of G. We compute all almost split sequences over kG when kG is of finite representation type, or more generally, for a finite dimensional k-algebra $ \Lambda $ given by a Brauer tree. We apply this to show that if $ \Lambda $ and $ \Lambda '$ are stably equivalent k-algebras given by Brauer trees, then they have the same number of simple modules.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0573041-3
PII: S 0002-9947(1977)0573041-3
Article copyright: © Copyright 1977 American Mathematical Society