English

On the relation between cluster and classical tilting

Representation Theory 2008-10-03 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0810.0411,
  title  = {On the relation between cluster and classical tilting},
  author = {Thorsten Holm and Peter Jorgensen},
  journal= {arXiv preprint arXiv:0810.0411},
  year   = {2008}
}

Comments

20 pages

R2 v1 2026-06-21T11:26:41.345Z