The Classification of the Trivial Source Modules in Blocks with Cyclic Defect Groups

Abstract

Relying on the classification of the indecomposable liftable modules in arbitrary blocks with non-trivial cyclic defect groups by the first author and Naehrig we give a complete classification of the trivial source modules lying in such blocks, describing in particular their associated path on the Brauer tree of the block in the sense of Janusz’ classification of the indecomposable modules of such blocks. Furthermore, the appendix contains a minor correction to the statement of the classification theorem of the indecomposable liftable modules, as well as a description of the minimal distance from an arbitrary indecomposable liftable module to the boundary of the stable Auslander-Reiten quiver of the block.