Torsion pairs in a triangulated category generated by a spherical object

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, $T_w$, generated by a w-spherical object for any integer w. Inspired by the combinatorics of $T_w$ for w < 0, we also characterise the torsion pairs in a certain w-Calabi-Yau orbit category of the bounded derived category of the path algebra of Dynkin type A.

v2: 36 pages, 11 figures, added Section 4 which deals with extensions whose outer terms are decomposable, minor changes in presentation, accepted in J. Algebra