Auslander correspondence for triangulated categories

Hanihara, Norihiro

doi:10.2140/ant.2020.14.2037

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Auslander correspondence for triangulated categories

Norihiro Hanihara

Vol. 14 (2020), No. 8, 2037–2058

DOI: 10.2140/ant.2020.14.2037

Abstract

We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism algebras as the Auslander algebras. For the second one, we introduce the notion of $[1]$ -additive generators and consider their graded endomorphism algebras as the Auslander algebras. We give a homological characterization of the Auslander algebras for each class. Along the way, we also show that the algebraic triangle structures on the homotopy categories are unique up to equivalence.

Keywords

triangulated category, Auslander correspondence, periodic algebra, Cohen–Macaulay module

Mathematical Subject Classification 2010

Primary: 18E30

Secondary: 16E05, 16E65, 16G70

Milestones

Received: 28 September 2018

Revised: 1 December 2019

Accepted: 23 April 2020

Published: 18 September 2020

Authors

Norihiro Hanihara
Graduate School of Mathematics Nagoya University Furocho, Chikusa-ku Nagoya Japan

Vol. 14, No. 8, 2020