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arXiv · 2206.12875

Backstr\"om algebras

Yuriy A. Drozd
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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 $2$. 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 Backstr\"om pair to a ring of triangular matrices and define the global dimension of the latter.

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BibTeXRIS

Yuriy A. Drozd. 2022-06-26. Backstr\"om algebras. https://doi.org/10.2140/pjm.2023.323.67

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