Maximal 𝑛-orthogonal modules for selfinjective algebras

Erdmann, Karin; Holm, Thorsten

doi:10.1090/S0002-9939-08-09297-6

Maximal $n$-orthogonal modules for selfinjective algebras
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Proc. Amer. Math. Soc. 136 (2008), 3069-3078 Request permission

Abstract:

Let $A$ be a finite-dimensional selfinjective algebra. We show that, for any $n\ge 1$, maximal $n$-orthogonal $A$-modules (in the sense of Iyama) rarely exist. More precisely, we prove that if $A$ admits a maximal $n$-orthogonal module, then all $A$-modules are of complexity at most 1.

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