On the number of tilting modules over a class of Auslander algebras

Abstract

Let [Formula: see text] be a radical square zero algebra of a Dynkin quiver and let [Formula: see text] be the Auslander algebra of [Formula: see text]. Then the number of tilting right [Formula: see text]-modules is [Formula: see text] if [Formula: see text] is of [Formula: see text] type for [Formula: see text]. Otherwise, the number of tilting right [Formula: see text]-modules is [Formula: see text] if [Formula: see text] is either of [Formula: see text] type for [Formula: see text] or of [Formula: see text] type for [Formula: see text].