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Closedness of star products and cohomologies. (English) Zbl 0853.58058

Brylinski, Jean-Luc (ed.) et al., Lie theory and geometry: in honor of Bertram Kostant on the occasion of his 65th birthday. Invited papers, some originated at a symposium held at MIT, Cambridge, MA, USA in May 1993. Boston, MA: Birkhäuser. Prog. Math. 123, 241-259 (1994).
The paper is centered at the notion of so-called closed star products and its relations with cyclic cohomologies and index theorems. This is connected with geometric quantization, and the authors explain how quantum groups (in their topological form) are examples of star products. The paper also introduces star products, deformations of Poisson brackets and various cohomologies related to them.
For the entire collection see [Zbl 0807.00014].

MSC:

53D50 Geometric quantization
58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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