Hochschild cohomology and deformation quantization of affine toric varieties

For an affine toric variety Spec(A), we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Under certain assumptions we compute the dimensions of the Hodge summands T-(i)(1) (A), generalizing the existing results about the Andre Quillen cohomology group T-(1)(1) (A). We prove that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization. (C) 2018 Elsevier Inc. All rights reserved.