Vol. 14, No. 8, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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