
TL;DR
This paper introduces Backström pairs and rings, explores their derived categories, and establishes bounds on their global and derived dimensions, providing new categorical and homological insights.
Contribution
It defines Backström pairs and rings, studies their derived categories, and constructs categorical resolutions and semi-orthogonal decompositions.
Findings
Derived dimension of Backström rings is at most 2
Constructed categorical resolutions for Backström rings
Established semi-orthogonal decomposition of derived categories
Abstract
We introduce Backstr\"om pairs and Backstr\"om 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 Backstr\"om ring is at most . 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 Backstr\"om pair to a ring of triangular matrices and define the global dimension of the latter.
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Taxonomy
TopicsAdvanced Topics in Algebra · Catalysis and Oxidation Reactions · Advanced Algebra and Logic
