Torsion pairs in a triangulated category generated by a spherical object

Coelho Simoes, Raquel and Pauksztello, David (2016) Torsion pairs in a triangulated category generated by a spherical object. Journal of Algebra, 448. pp. 1-47. ISSN 0021-8693

Abstract

We extend Ng's characterisation of torsion pairs in the 2-Calabi–Yau triangulated category generated by a 2-spherical object to the characterisation of torsion pairs in the w-Calabi–Yau triangulated category, Tw, generated by a w-spherical object for any w∈Z. Inspired by the combinatorics of Tw for w⩽−1, we also characterise the torsion pairs in certain negative Calabi–Yau orbit categories of the bounded derived category of the path algebra of Dynkin type A.