Backström algebras

Yuriy Drozd

Vol. 323 (2023), No. 1, 67–88

DOI: 10.2140/pjm.2023.323.67

Abstract

We introduce Backström pairs and Backström rings, study their derived categories and construct for them a sort of categorical resolutions. For the latter we define the global dimension, construct a sort of semiorthogonal decomposition of the derived category and deduce that the derived dimension of a Backström ring is at most $2$. Using this semiorthogonal decomposition, we define a description of the derived category as the category of elements of a special bimodule. We also construct a partial tilting for a Backström pair to a ring of triangular matrices and define the global dimension of the latter.

Keywords

Backström rings, Backström pairs, derived categories, partial tilting

Mathematical Subject Classification

Primary: 16E35

Secondary: 16E10, 18G80

Milestones

Received: 28 June 2022

Revised: 14 February 2023

Accepted: 8 April 2023

Published: 29 May 2023