Maximal 𝑛-orthogonal modules for selfinjective algebras

Abstract

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