Maximal rigid subcategories in 2-Calabi-Yau triangulated categories
arXiv:1004.5475
Abstract
We study the maximal rigid subcategories in CY triangulated categories and their endomorphism algebras. Cluster tilting subcategories are obviously maximal rigid; we prove that the converse is true if the CY triangulated categories admit a cluster tilting subcategory. As a generalization of a result of [KR], we prove that any maximal rigid subcategory is Gorenstein with Gorenstein dimension at most 1. Similar as cluster tilting subcategory, one can mutate maximal rigid subcategories at any indecomposable object. If two maximal rigid objects are reachable via mutations, then their endomorphism algebras have the same representation type.
14pages, fix many typos, add two references