Closedness of star products and cohomologies
Mosh\'e Flato, Daniel Sternheimer
TL;DR
This paper reviews star products, their relation to cohomologies, and explores closed star products, cyclic cohomology, index theorems, and their connection to quantum groups in a comprehensive manner.
Contribution
It provides a detailed analysis of closed star products and their links to cyclic cohomology, index theorems, and quantum groups, highlighting their mathematical significance.
Findings
Closed star products are closely related to cyclic cohomology.
Quantum groups can be understood as examples of star products.
The paper clarifies the role of cohomologies in deformation quantization.
Abstract
We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra