Claus Michael Ringel
Abstract: A triangulated category is called hereditary provided it is equivalent to the bounded derived category of a hereditary abelian category using an equivalence which respects the translation functor. Such a category has a very lucid additive structure. An old preprint of mine (from 1998) was devoted to these categories, but pretended to recover the triangulated structure of such a category. Based on suggestions by Michel Van den Bergh, Xiao-Wu Chen has now shown that a hereditary triangulated which is algebraic is triangle equivalent to the bounded derived category of a hereditary abelian category. It is an open question whether any hereditary triangulated category is algebraic. The lecture will provide a survey on some of the properties of hereditary triangulated categories. It is based on a forthcoming joint paper with Xiao-Wu Chen. Ringel Last modified: August 26, 2015