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

Abstract

Let [Formula: see text] be a radical square zero Nakayama algebra with [Formula: see text] simple modules and let [Formula: see text] be the Auslander algebra of [Formula: see text]. Then every indecomposable direct summand of a tilting [Formula: see text]-module is either simple or projective. Moreover, if [Formula: see text] is self-injective, then the number of tilting [Formula: see text]-modules is [Formula: see text]; otherwise, the number of tilting [Formula: see text]-modules is [Formula: see text].