Parametrizing equivalence classes of invariant star products. (English) Zbl 0943.53051

Bertelson, Mélanie; Bieliavsky, Pierre; Gutt, Simone

Lett. Math. Phys. 46, No. 4, 339-345 (1998).

Authors’ abstract: “Let \((M,\omega,\nabla)\) be a symplectic manifold endowed with a symplectic connection \(\nabla\). Let \(\text{Symp}(M,\omega)\) be the group of symplectic transformations of \((M,\omega)\) and \(\text{Aff}(M,\nabla)\) be the group of affine transformations of the affine manifold \((M,\nabla)\). In this letter, we show that, for any subgroup \(G\) of \(\text{Symp}(M,\omega)\cap \text{Aff}(M,\nabla)\), the set of \(G\)-equivalence classes of \(G\)-invariant star products on \((M,\omega)\) is canonically parametrized by the set of sequences of elements belonging to the second de Rham cohomology space of the \(G\)-invariant de Rham complex on \(M\)”.

MSC:

53D55	Deformation quantization, star products
37J05	Relations of dynamical systems with symplectic geometry and topology (MSC2010)
81S10	Geometry and quantization, symplectic methods

Keywords:

deformation quantization; invariant star product; symplectic manifold; symplectic transformation; subgroup; deRham cohomology