Morita equivalence in deformation quantization | Posted on:2002-09-16 | Degree:Ph.D | Type:Dissertation | University:University of California, Berkeley | Candidate:Bursztyn, Henrique | Full Text:PDF | GTID:1465390011990521 | Subject:Mathematics | Abstract/Summary: | | In this dissertation we study the notion of Morita equivalence in the realm of formal deformation quantization of Poisson manifolds. We show that Rieffel's construction of induced representations of C*-algebras and the notion of strong Morita equivalence can be extended to a wider class of *-algebras, including those arising in deformation quantization. In order to study strong Morita equivalence in the framework of deformation quantization, we consider finitely generated projective inner-product modules over hermitian star-product algebras. These objects are quantum analogs of hermitian vector bundles and are obtained from them through a deformation quantization procedure. In this work, we define and study deformation quantization of hermitian vector bundles and show how they produce examples of strongly Morita equivalent deformed *-algebras. Finally, we present a study of the classification of star products on a Poisson manifold M up to Morita equivalence. We show how deformation quantization of line bundles over M produces a canonical action Φ of the Picard group Pic(M ) ≅ H2(M,) on the moduli space of equivalence classes of differential star products on M, in such a way that two star products are Morita equivalent if and only if they lie in the same Φ-orbit. We describe the semiclassical limit of Φ explicitly in terms of the characteristic classes of star products by studying contravariant connections arising in the semiclassical limit of line bundle deformations. | Keywords/Search Tags: | Deformation, Morita equivalence, Star products | | Related items |
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