On the relation between cluster and classical tilting

Details On the relation between cluster and classical tilting On the relation between cluster and classical tilting

2008-10-02

arxiv.org/abs/0810.0411v1

Mathematics

Representation Theory

20 pages

Scientific paper

Let D be a triangulated category with a cluster tilting subcategory U. The quotient category D/U is abelian; suppose that it has finite global dimension. We show that projection from D to D/U sends cluster tilting subcategories of D to support tilting subcategories of D/U, and that, in turn, support tilting subcategories of D/U can be lifted uniquely to maximal 1-orthogonal subcategories of D.

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