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Abstract Poisson structures and star-products. (English) Zbl 0791.58039
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 387-394 (1992).
It is well-known that the existence of star products on every symplectic manifold was proved by M. de Wilde and P. Lecomte [Lett. Math. Phys. 7, 487-496 (1983; Zbl 0526.58023)]. The natural question is to extend their result to the general case of nonsymplectic manifolds.
In the paper under review the author presents a purely algebraic approach to this question, which gives us a generalization of the Vey-Moyal product and can be applied in many nonsymplectic cases.
For the entire collection see [Zbl 0764.00002].
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems