The Stable Monomorphism Category of a Frobenius category
By Xiao-Wu Chen. 2009
52 citations recorded by the source corpus.
For a Frobenius abelian category $\mathcal{A}$, we show that the category ${\rm Mon}(\mathcal{A})$ of monomorphisms in $\mathcal{A}$ is a Frobenius exact category; the associated stable category $\underline{\rm Mon}(\mathcal{A})$ modulo projective objects is called the stable monomorphism category of $\mathcal{A}$. We show that a tilting object in the stable category $\underline{\mathcal{A}}$ of $\mathcal{A}$ modulo projective objects induces naturally a tilting object in $\underline{{\rm Mon}}(\mathcal{A})$. We show that if $\mathcal{A}$ is the category of (graded) modules over a (graded) self-injective algebra $A$, then the stable monomorphism category is triangle equivalent to the (graded) singularity category of the (graded) $2\times 2$ upper triangular matrix algebra $T_2(A)$. As an application, we give two characterizations to the stable category of Ringel-Schmidmeier (\cite{RS3}).
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/99c8dbdfd02e2ae9e2dcc94cf22a161584f7b725
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In Algebra and Number Theory
- Nan Gao
- Chrysostomos Psaroudakis
- Pu Zhang
- Bao-Lin Xiong
- Yuehui Zhang
- D. Kussin
- H. Lenzing
- H. Meltzer
In Geometry and Topology
- Nan Gao
- Pu Zhang
- Chrysostomos Psaroudakis
- D. Kussin
- H. Lenzing
- H. Meltzer
- Bao-Lin Xiong
- Yuehui Zhang
In Statistical and Nonlinear Physics
- Chrysostomos Psaroudakis
- Nan Gao
- Pu Zhang
- Bao-Lin Xiong
- D. Kussin
- H. Lenzing
- H. Meltzer
- Xiao-Wu Chen
Citations in the corpus
- Auslander–Reiten translations in monomorphism categories (2011, background): “Chen [C] shows that S2(A) of a Frobenius abelian category A is a Frobenius exact category.”
- Nilpotent operators and weighted projective lines (2010, methodology): “Independently this tilting object in S̃(p) was constructed by Xiao-Wu Chen [4] with a direct argument not relying on Theorem C.”
- Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings (2015, background): “In fact, there are connections with classification problems (Ringel, Schmidmeier [40–42], Xiong, Zhang, Zhang [45]), with weighted projective lines (Kussin, Lenzing, Meltzer [31]), and with aspects of Gorenstein homological algebra (Beligiannis [10, 11], Zhang [49], Chen [17]).”