CONSISTENCY CONDITIONS FOR DIMER MODELS

By Raf Bocklandt. Glasgow Mathematical Journal, 2011

61 citations recorded by the source corpus.

Abstract Dimer models are a combinatorial tool to describe certain algebras that appear as noncommutative crepant resolutions of toric Gorenstein singularities. Unfortunately, not every dimer model gives rise to a noncommutative crepant resolution. Several notions of consistency have been introduced to deal with this problem. In this paper, we study the major different notions in detail and show that for dimer models on a torus, they are all equivalent.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a825ddee8c54e9d6622e771e67d9141bb942bc81

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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

• A geometric model for the derived category of gentle algebras (2018, unknown): “lgebras first appeared in the form of iterated tilted algebras of type A[6, 7] and type A˜ [8]. It has transpired since that they naturally appear in many different contexts; these include dimer models [21, 22], enveloping algebras of Lie algebras [49], and cluster theory, where they appear as m-clust”
• Dimer models and cluster categories of Grassmannians (2013, methodology): “Following [ 2 , § 6], we make the following definition (noting that Bocklandt uses the term ‘embedding with isoradial cycles’).”