Equivalence of star products. (English) Zbl 0881.58021

Bertelson, Mélanie; Cahen, Michel; Gutt, Simone

Classical Quantum Gravity 14, No. 1A, A93-A107 (1997).

Summary: We give an elementary proof of the fact that equivalence classes of smooth or differentiable star products on a symplectic manifold \(M\) are parametrized by sequences of elements in the second de Rham cohomology space of the manifold. The parametrization is given explicitly in terms of Fedosov’s construction which yields a star product when one chooses a symplectic connection and a sequence of closed 2-forms on \(M\). We also show how derivations of a given star product, modulo inner derivations, are parametrized by sequences of elements in the first de Rham cohomology space of \(M\).

MSC:

37J99

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

equivalence; star products; symplectic manifold; de Rham cohomology space; parametrization