Backström algebras

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 semi-orthogonal decomposition of the derived category and deduce that the derived dimension of a Backström ring is at most $2$. Using this semi-orthogonal decomposition, we define a description of the module 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.

24 pages