Letters in Mathematical Physics

, Volume 69, Issue 1, pp 223–235 | Cite as

The Picard Groupoid in Deformation Quantization



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 i2=−1 to the *-representation theory of *-algebras over 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


Deformation quantization Representation theory Morita equivalence Picard groupoid 


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© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Fakultät für Mathematik und PhysikAlbert-Ludwigs-Universität Freiburg, Physikalisches InstitutFreiburgGermany

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