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arXiv · 1404.1976

Maximal rigid objects without loops in connected 2-CY triangulated categories are cluster-tilting objects

Jinde Xu·Baiyu Ouyang
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Abstract

In this paper, we study the conjecture II.1.9 of Cluster structures for 2-Calabi-Yau categories and unipotent groups, which said that any maximal rigid object without loops or 2-cycles in its quiver is a cluster tilting object in a connected Hom-finite triangulated 2-CY category C. We obtain some conditions equivalent to the conjecture, and using them we proved the conjecture.

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BibTeXRIS

Jinde Xu, Baiyu Ouyang. 2014-08-30. Maximal rigid objects without loops in connected 2-CY triangulated categories are cluster-tilting objects. https://doi.org/10.1142/s0219498815500711

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