Deformation quantization modules II. Hochschild class

2008/09/25 by Masaki Kashiwara, Pierre Schapira, Kashiwara, Masaki +1 · 1 citation
Mathematics · #32C38 #46L65 #53D55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.0809.4309

openalex publication_date 2008/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Mukai pairing, I: the Hochschild structure

Cited by

• A noncommutative geometric approach to the quantum structure of spacetime

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