Singularity categories, Schur Functors and Triangular Matrix Rings

Details Singularity categories, Schur Functors and Triangular Matrix Rings Singularity categories, Schur Functors and Triangular Matrix Rings

2007-06-25

arxiv.org/abs/0706.3638v1

Algebra and Repre. Th. 12 (2009) 181-191.

Mathematics

Representation Theory

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Scientific paper

We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz-Happel's theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen-Macaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed.

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