2001/05/01 by Henrique Bursztyn, Bursztyn, Henrique · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math-ph #math.MP #math.QA #math.SG #msc:53D17 #msc:53D55
paper · pdf · doi:10.48550/arxiv.math/0105001
23 pages. Minor corrections made (Sec. 2.1), few typos fixed. Final version to appear at Internat. Math. Res. Notices
arxiv created 2002/01/15 · arxiv updated 2009/11/30
In this paper we show how deformation quantization of line bundles over a Poisson manifold M produces a canonical action Φ of the Picard group \Pic(M)≅ H2(M,\mathbb Z) on the moduli space of equivalence classes of differential star products on M, \Def(M). The orbits of Φ characterize Morita equivalent star products on M. We describe the semiclassical limit of Φ in terms of the characteristic classes of star products by studying the semiclassical geometry of deformed line bundles.