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

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.

15 pages. arXiv admin note: text overlap with arXiv:1004.5475, arXiv:math/0701557 by other authors. final version, to appear in J. Algebra Appl. minor changes

References in corpus (2)

• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Cluster structures for 2-Calabi-Yau categories and unipotent groups