The Picard groupoid in deformation quantization

Details The Picard groupoid in deformation quantization The Picard groupoid in deformation quantization

2003-12-05

arxiv.org/abs/math/0312118v1

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/s11005-004-0421-4

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.

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