Maximal rigid subcategories in 2-Calabi-Yau triangulated categories

Details Maximal rigid subcategories in 2-Calabi-Yau triangulated categories Maximal rigid subcategories in 2-Calabi-Yau triangulated categories

2010-04-30

arxiv.org/abs/1004.5475v3

Mathematics

Representation Theory

14pages, fix many typos, add two references

Scientific paper

We study the maximal rigid subcategories in $2-$CY triangulated categories and their endomorphism algebras. Cluster tilting subcategories are obviously maximal rigid; we prove that the converse is true if the $2-$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.

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