The Picard groupoid in deformation quantization
Quantum Algebra
2009-11-10 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0312118,
title = {The Picard groupoid in deformation quantization},
author = {Stefan Waldmann},
journal= {arXiv preprint arXiv:math/0312118},
year = {2009}
}
Comments
LaTeX 2e, 10 pages. Talk given at the PQR 2003 Euro-Conference in June 2003, Brussels. Dedicated to Alan Weinstein for his 60th birthday