Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras

Research paper by Xiaojin Zhang

Indexed on: 15 Oct '20Published on: 14 Oct '20Published in: arXiv - Mathematics - Representation Theory


Let $\Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then every indecomposable direct summand of a tilting $\Gamma$-module is either simple or projective. Moreover, if $\Lambda$ is self-injective, then the number of tilting $\Gamma$-modules is $2^n$; otherwise, the number of tilting $\Gamma$-modules is $2^{n-1}$.