2005/04/13 by Martin Bordemann, Gregory Ginot, Bordemann, Martin +7
Mathematics · #16E40 #53D55 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16E40 #msc:53D55
paper · pdf · doi:10.48550/arxiv.math/0504276
56 pages (french). This is the widely extended version of a previous preprint math/0309321
arxiv created 2005/04/13 · arxiv updated 2009/12/01
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^∞(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 = Rn and C = Rn-l with l > 1 there are no obstructions to this formality.