On the relation between cluster and classical tilting

TY - JOUR

T1 - On the relation between cluster and classical tilting

AU - Holm, Thorsten

AU - Jørgensen, Peter

PY - 2010/9/1

Y1 - 2010/9/1

N2 - 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 weak cluster tilting subcategories of D.

AB - 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 weak cluster tilting subcategories of D.

UR - http://www.scopus.com/inward/record.url?scp=76049096719&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2009.11.012

DO - 10.1016/j.jpaa.2009.11.012

M3 - Journal article

AN - SCOPUS:76049096719

SN - 0022-4049

VL - 214

SP - 1523

EP - 1533

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 9

ER -