Singularity categories of gentle algebras

By Martin Kalck. 2012

71 citations recorded by the source corpus.

We determine the singularity category of an arbitrary finite‐dimensional gentle algebra Λ . It is a finite product of n ‐cluster categories of type A1 . Equivalently, it may be described as the stable module category of a self‐injective gentle algebra. If Λ is a Jacobian algebra arising from a triangulation T of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of T .

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d6610fd7c0065ea121b58f36851dfdcf556b10ec

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In Algebra and Number Theory

1. Guodong Zhou
2. Dawei Shen
3. Xiao-Wu Chen
4. Apostolos Beligiannis
5. P. Ara
6. Pu Zhang
7. Kulumani M. Rangaswamy

In Geometry and Topology

1. Guodong Zhou
2. Dawei Shen
3. Xiao-Wu Chen
4. Apostolos Beligiannis
5. P. Ara
6. Pu Zhang
7. Kulumani M. Rangaswamy

In Statistical and Nonlinear Physics

1. Guodong Zhou
2. Xiao-Wu Chen
3. Dawei Shen
4. Pu Zhang

Citations in the corpus

• The Gorenstein-projective modules over a monomial algebra (2015, background): “ σ∗ on the category kn-mod by twisting the module actions. We denote by Tn = (kn-mod,σ∗) the resulting triangulated category. The main result in this section is as follows. It is inspired by the work [15], and extends [15, Theorem 2.5(b)]. Theorem 5.7. Let A = kQ/I be a quadratic monomial algebra. A”