Séminaires : Séminaire d'Algèbre

We study self-orthogonal modules, i.e., modules T such that Ext^i(T, T) = 0 for all i > 0. We introduce projectively Wakamatsu-tilting modules (pW-tilting modules) as a generalization of tilting modules. If A is a representation-finite algebra, every self-orthogonal A-module can be completed to a pW-tilting module, and the following classes coincide: pW-tilting modules, Wakamatsu tilting modules, maximal self-orthogonal modules, and self-orthogonal modules T with |T| = |A|. We also prove that every self-orthogonal module over a representation-finite Iwanaga-Gorenstein algebra has finite projective dimension. We finally explain some open conjectures on self-orthogonal modules.