Deformations of the algebra of functions of a symplectic manifold. Comparison between Fedosov and de Wilde, Lecomte
\textit{M. de Wilde} and \textit{P. B. A. Lecomte} in their papers in Ann. Inst. Fourier 35, No. 2, 117-143 (1985; Zbl 0526.58023), Lett. Math. Phys. 7, 487-496 (1983; Zbl 0566.58039) and \textit{B. V. Fedosov} in his paper ``Formal quantization'' [Some topics of Modern Mathematics and their applications to problems of mathematical physics, Moscow, 129-136 (1985)] have proved that if \(M\) is a symplectic manifold, then there exists a deformation \(*_t\) of the product giving place to the symplectic Poisson brackets. The classifications of the classes of isomorphy of the above deformations \(*_t\) are given by Fedosov and also by De Wilde and Lecomte. The purpose of the present paper is to compare the applied methods, the corresponding classifications and also to explain the effect of a change of formal parameter \(t \to \sum^\infty_1 a_nt^n\) with \(a_1\) invertible.
scientific article; zbMATH DE number 894937