On the tilting complexes for the Auslander algebra of the truncated polynomial ring

Abstract

We give a bijection between the tilting complexes in the bounded homotopy category of the Auslander algebra of the truncated polynomial ring and ZxB where B is the Artin braid goup of type A with n-1 generators. The tilting complexes have mutation components parametrized by Z and each component has a natural faithful and transitive operation of B. This also implies that the derived Picard group of this algebra is isomorphic to the direct product of its outer isomorphism group and ZxB. This work is to be seen as a continuation of the work of Geuenich and an application of the work of Aihara and Mizuno on tilting complexes of preprojective algebras of Dynkin type.