Tuesday, December 5, 15:30, 7.527.
Torkil Stai (NTNU Trondheim)
Orbit categories and periodic complexes.
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