Formalite $G_\infty$ adaptee et star-representations sur des sous-varietes coisotropes

Details Formalite $G_\infty$ adaptee et star-representations sur des sous-varietes coisotropes Formalite $G_\infty$ adaptee et star-representations sur des sous-varietes coisotropes

2005-04-13

arxiv.org/abs/math/0504276v1

Mathematics

Quantum Algebra

56 pages (french). This is the widely extended version of a previous preprint math/0309321

Scientific paper

Let X be a Poisson manifold and C a coisotropic submanifold and let I be the vanishing ideal of C. In this work we want to construct a star product * on X such that I[[lambda]] is a left ideal for *. Thus we obtain a representation of the star product algebra A[[lambda]] = C^\infty(X)[[lambda]] on B[[lambda]] = A[[lambda]] / I[[lambda]] deforming the usual representation of A on the functions on C. The result follows from a generalization of Tamarkin's formality adapted to the submanifold C. We show that in the case X = R^n and C = R^{n-l} with l > 1 there are no obstructions to this formality.

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