Torsion pairs in a triangulated category generated by a spherical object

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, TwTw, generated by a w  -spherical object for any w∈Zw∈Z. Inspired by the combinatorics of TwTw for w⩽−1w⩽−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.