Maximal rigid objects without loops in connected 2-CY triangulated categories are cluster-tilting objects
Representation Theory
2014-09-02 v2
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.
Keywords
Cite
@article{arxiv.1404.1976,
title = {Maximal rigid objects without loops in connected 2-CY triangulated categories are cluster-tilting objects},
author = {Jinde Xu and Baiyu Ouyang},
journal= {arXiv preprint arXiv:1404.1976},
year = {2014}
}
Comments
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