Dimer models provide a method of constructing noncommutative crepant resolutions of affine toric Gorenstein threefolds. In homological mirror symmetry, they can also be used to describe noncommutative Landau–Ginzburg models dual to punctured Riemann surfaces. For a consistent dimer embedded in a torus, we explicitly compute the Hochschild cohomology of its Jacobi algebra in terms of dimer combinatorics. This includes a full characterization of the Batalin–Vilkovisky structure induced by the Calabi–Yau structure of the Jacobi algebra. We then compute the compactly supported Hochschild cohomology of the category of matrix factorizations for the Jacobi algebra with its canonical potential.

二聚体模型提供了一种构建仿射复曲面 Gorenstein 三重非交换蠕变分辨率的方法。在同调镜面对称中，它们也可用于描述非对易的 Landau-Ginzburg 模型与穿孔黎曼曲面对偶。对于嵌入圆环中的一​​致二聚体，我们根据二聚体组合明确计算其雅可比代数的 Hochschild 上同调。这包括对由雅可比代数的 Calabi-Yau 结构引起的 Batalin-Vilkovisky 结构的完整表征。然后，我们计算雅可比代数的矩阵分解范畴的紧支持 Hochschild 上同调及其规范势。