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Torsion pairs in a triangulated category generated by a spherical object

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arxiv 1404.4623 v2 pith:V7RDL26X submitted 2014-04-17 math.RT math.CO

Raquel Coelho Simoes , David Pauksztello This is my paper · ORCID
classification math.RTmath.CO
keywords categorypairstorsiongeneratedobjecttriangulatedcharacterisationspherical
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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.

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  1. Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory

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    The paper constructs infinite discrete Nakayama representations via persistence theory and stabilizes them into negative Calabi-Yau versions of Igusa-Todorov discrete cluster categories of type A, with geometric model...

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