The Picard groupoid in deformation quantization

Abstract

In this letter we give an overview on recent developments in representation theory of star product algebras. In particular, we relate the *-representation theory of *-algebras over rings C = R(i) with an ordered ring R and i^2 = -1 to the *-representation theory of *-algebras over \mathbb{C} and point out some properties of the Picard groupoid corresponding to the notion of strong Morita equivalence. Some Morita invariants are interpreted as arising from actions of this groupoid.

LaTeX 2e, 10 pages. Talk given at the PQR 2003 Euro-Conference in June 2003, Brussels. Dedicated to Alan Weinstein for his 60th birthday

References in corpus (3)

• Picard groups in Poisson geometry
• Completely positive inner products and strong Morita equivalence
• Bimodule deformations, Picard groups and contravariant connections

Cited by in corpus (8)

• States and representations in deformation quantization
• The simplicial interpretation of bigroupoid 2-torsors
• Noncommutative field theories from a deformation point of view
• H-äquivariante Morita-Äquivalenz und Deformationsquantisierung
• Induction of representations in deformation quantization
• The Covariant Picard Groupoid in Differential Geometry
• Covariant Strong Morita Theory of Star Product Algebras
• The H-Covariant Strong Picard Groupoid