Dimer models and Hochschild cohomology (Q2042930)

Let us recall that dimer models can be used to construct noncommutative crepant resolutions and to describe noncommutative Laudau-Ginzburg models. In this paper, for a consistent dimer embeded in a torus, the author explicitly computes the Hochschild cohomology of its Jacobi algebra in terms of dimer combinatorics. The author fist reviews dimer models, Calabi-Yau algebras, matrix factorizations and Hochschild cohomology. Then, he obtains a full characterization of the Batalin-Vilkovisky structure induced by the Calabi-Yau structure of the Jacobi algebra. The Hochschild cohomology corresponding of matric factorizations for the Jacobi algebra is also computed.