Torkil Stai (NTNU Trondheim)

Orbit categories and periodic complexes.

Abstract:

Let T be a triangulated category with an automorphism F. By keeping the objects and naively "blowing up" the morphism spaces of T, we obtain the orbit category T/F in which each object x becomes isomorphic to Fx. It is then only natural to ask whether there is a triangulated structure on T/F which is compatible with the one on T. In the algebraic setting, this question can be rephrased by appealing to the enhancing level; the differential graded framework lets us embed T/F in a canonical 'triangulated hull'. The aim of this talk is to explain how we can explicitly understand said embedding in the case that T is the bounded derived category of an algebra and F is cohomological shift. As one application, we will see a simple example where the above isomorphism between x and Fx cannot be natural.