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The Picard groupoid in deformation quantization. (English) Zbl 1065.53070
The paper under review is divided into six sections. Section 1 is a short introduction where the author clarifies the picture of his paper. Section 2 presents some motivations for the study of *-representations. The notion of positivity makes the object of section 3. Section 4 deals with the study of pre-Hilbert modules and their tensor products. In section 5 he presents the strong Morita equivalence and its corresponding Picard groupoid. Finally, the last section proves how some Morita invariants can be seen as arising from actions of the Picard groupoid. In conclusion, a very nice paper.

MSC:
53D55 Deformation quantization, star products
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