Tilting modules over Auslander algebras of Nakayama algebras with radical cube zero

Abstract

Let A′ be the Auslander algebra of a finite dimensional basic connected Nakayama algebra A with radical cube zero and n simple modules. Then the cardinality #tiltA′ of the set consisting of isomorphism classes of basic tilting A′-modules is #tiltA′ = \uf8f1\uf8f2\uf8f4\uf8f3 (1 + √ 2)2n−2 − (1− √ 2)2n−2 2 √ 2 , if A is non-self-injective with n ≥ 4; √ [(1 + √ 2)2n − (1− √ 2)2n]2 + 4, if A is self-injective with n ≥ 2.