Almost split sequences for group algebras of finite representation type

Reiten, Idun

doi:10.1090/S0002-9947-1977-0573041-3

Almost split sequences for group algebras of finite representation type
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Trans. Amer. Math. Soc. 233 (1977), 125-136 Request permission

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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