Bimodule deformations, Picard groups and contravariant connections

Henrique Bursztyn, Stefan Waldmann

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

英文摘要：

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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