A categorification of Grassmannian cluster algebras

By B. T. Jensen, A. King, Xiuping Su. 2013

86 citations recorded by the source corpus.

We describe a ring whose category of Cohen–Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k ‐planes in n ‐space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective–injective object is Geiss–Leclerc–Schröer's category Sub Qk , which categorifies the coordinate ring of the big cell in this Grassmannian.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8864e056698e51f6f5c48fcce84b2e5cc0ec0edc

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In Discrete Mathematics and Combinatorics

1. Karin Baur
2. B. Marsh
3. A. King
4. B. Keller
5. I. Reiten
6. Aslak Bakke Buan

In Geometry and Topology

1. Karin Baur
2. B. Marsh
3. A. King
4. Ralf Schiffler
5. B. Keller
6. Osamu Iyama
7. I. Reiten
8. Aslak Bakke Buan

In Mathematical Physics

1. Karin Baur
2. B. Marsh
3. A. King
4. Ralf Schiffler
5. Osamu Iyama
6. Hugh Thomas
7. I. Reiten
8. B. Keller

Citations in the corpus

• Dimer models and cluster categories of Grassmannians (2013, methodology): “Recently Jensen-King-Su [19] have given a full and direct categorification of the cluster structure on the homogeneous coordinate ring, using the category of (maximal) CohenMacaulay modules over the completion of an algebra B, which is a quotient of the preprojective algebra of type Ãn−1.”