Classification of co-slicings and co-t-structures for the Kronecker algebra

Jorgensen, Peter and Pauksztello, David (2015) Classification of co-slicings and co-t-structures for the Kronecker algebra. Journal of Pure and Applied Algebra, 219 (3). pp. 569-590. ISSN 0022-4049

Abstract

In this paper we introduce the notion of a ‘generalised’ co-slicing of a triangulated category. This generalises the theory of co-stability conditions in a manner analogous to the way in which Gorodentsev, Kuleshov and Rudakov's t-stabilities generalise Bridgeland's theory of stability conditions. As an application of this notion, we use a complete classification of ‘generalised’ co-slicings in the bounded derived category of the Kronecker algebra, Db(KQ), to obtain a classification of co-t-structures in Db(KQ). This is then used to compute the co-stability manifold of Db(KQ).