Singularity Categories, Schur Functors and Triangular Matrix Rings
By Xiao-Wu Chen. 2007
77 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ab44a5e6ebc97fda019cd4d996f8081dc818b966
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In Algebra and Number Theory
- Oyvind Solberg
- Oystein Skartsaeterhagen
- Chrysostomos Psaroudakis
- Xiao-Wu Chen
- Apostolos Beligiannis
- Nan Gao
- P. Ara
- Pu Zhang
In Geometry and Topology
- Oyvind Solberg
- Oystein Skartsaeterhagen
- Chrysostomos Psaroudakis
- Xiao-Wu Chen
- Apostolos Beligiannis
- Nan Gao
- P. Ara
- Pu Zhang
In Statistical and Nonlinear Physics
Citations in the corpus
- The singularity category of an algebra with radical square zero (2011, background): “A criterion on the Hom-finiteness of the singularity category is given in terms of the valued quiver of the artin algebra.”
- Algebras with radical square zero are either self-injective or CM-free (2011, background): “In general, there are Gorenstein algebras which are neither self-injective nor of finite global dimension ([14, 8]).”
- Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements (2014, background): “Note that in the first statement we recover a theorem by Chen [15].”