Equivalence of star products

Details Equivalence of star products Equivalence of star products

Jan 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997cqgra..14a..93b&link_type=abstract

Classical and Quantum Gravity, Volume 14, Issue 1A, pp. A93-A107 (1997).

Physics

14

Scientific paper

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.

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