Selfextensions of modules for Nakayama and Brauer tree algebras

Abstract

For Nakayama algebras $A$, we prove that in case $Ex{t}_A^1(M,M)\ne 0$ for an indecomposable $A$-module $M$, we have that the projective dimension of $M$ is infinite. As an application we give a new proof of a classical result from \cite{Gus} on bounds of the Loewy length for Nakayama algebras with finite global dimension. For Brauer tree algebras $A$ with an indecomposable module $M$, we prove that $Ex{t}_A^1(M,M)\ne 0$ implies $Ex{t}_A^i(M,M)\ne 0$ for all $i>0$.

This article is not intended for publication and the main results will be soon generalised in a new project