Work

From triangulated categories to module categories via localisation

Year: 2012

Type: article

Abstract: We show that the category of finite dimensional modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category is equivalent to the Gabriel-Zisman localisation of the category with respect to a certain class of maps. This generalises the 2 2 -Calabi-Yau tilting theorem of Keller-Reiten, in which the module category is obtained as a factor category, to the rigid case.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/s0002-9947-2012-05631-5

Authors: Aslak Buan, Bethany Marsh

Institutions: Norwegian University of Science and Technology, University of Leeds

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Engineering and Physical Sciences Research Council

Awards: Cluster-tilting theory, G4776928572