Bimodule deformations, Picard groups and contravariant connections

Details Bimodule deformations, Picard groups and contravariant connections Bimodule deformations, Picard groups and contravariant connections

2002-07-26

arxiv.org/abs/math/0207255v2

Mathematics

Quantum Algebra

32 pages. Minor corrections in Sections 5 and 6, typos fixed. Revised version to appear in K-theory

Scientific paper

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K_0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on formal deformation quantization of Poisson manifolds by star products.

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