arXiv math/01050012001-05math.QAmath-phmath.MPmath.SG

Semiclassical Geometry of Quantum Line Bundles and Morita Equivalence of Star Products

Henrique Bursztyn

备注：: 23 pages. Minor corrections made (Sec. 2.1), few typos fixed. Final version to appear at Internat. Math. Res. Notices

英文摘要：

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 $\Pic(M)\cong H^2(M,\mathbb Z)$ 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.

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