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2020 Auslander correspondence for triangulated categories
Norihiro Hanihara
Algebra Number Theory 14(8): 2037-2058 (2020). 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.

Citation

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Norihiro Hanihara. "Auslander correspondence for triangulated categories." Algebra Number Theory 14 (8) 2037 - 2058, 2020. https://doi.org/10.2140/ant.2020.14.2037

Information

Received: 28 September 2018; Revised: 1 December 2019; Accepted: 23 April 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172701
Digital Object Identifier: 10.2140/ant.2020.14.2037

Subjects:
Primary: 18E30
Secondary: 16E05 , 16E65 , 16G70

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

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 8 • 2020
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