Bimodule deformations, Picard groups and contravariant connections. (English) Zbl 1054.53101

Bursztyn, Henrique; Waldmann, Stefan

\(K\)-Theory 31, No. 1, 1-37 (2004).

Authors summary : 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.

Reviewer: Benjamin Cahen (Metz)

MSC:

53D55	Deformation quantization, star products
16D90	Module categories in associative algebras
19M05	Miscellaneous applications of \(K\)-theory

Keywords:

bimodule deformation; deformation quantization; Morita equivalence; Picard group