Flat Poisson manifolds and finite-dimensional pseudogroups (Q1262601)

Continuing his paper [Izv. Akad. Nauk SSSR, Ser. Mat. 50, No.3, 508-538 (1986; Zbl 0608.58023)], the author completes a Poisson manifold N with the so called finite pseudogroup G realized by certain symplectical transformations of N. (The multiplication \(G\times G\to G\) is anomalous in the sense that it is depending on the parameter point \(\xi\in N.)\) Then the Lie algebra of infinitesimal actions on N generates a flat linear connection (and conversely). Moreover \(G\times N\) turns into a symplectic manifold with induced symplectic G-actions. The torsion of the connection (caused by the noncommutativity of the algebra) can be used for quantization.