Deformation quantization modules II. Hochschild class

Abstract

This paper is the continuation of arXiv:0802.1245. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and prove that the Hochschild class of the convolution of two coherent modules is the convolution of their Hochschild classes. We study with some details the case of symplectic deformations.

The contents of this paper is now included in Deformation quantization modules (arXiv:1003.3304).

References in corpus (2)

• The relative Riemann-Roch theorem from Hochschild homology
• The Mukai pairing, I: a categorical approach

Cited by in corpus (5)

• Deformation quantization modules I:Finiteness and duality
• Regular holonomic D[[h]]-modules
• Projective module description of embedded noncommutative spaces
• Deformations of algebroid stacks
• A noncommutative geometric approach to the quantum structure of spacetime