Vol. 14, No. 8, 2020

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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.

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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