Completely positive inner products and strong Morita equivalence.(English)Zbl 1111.53071

This paper unifies strong Morita equivalence and completely positive inner products in a general framework. Two types of structures are considered in this work: $$C^*$$ algebras and Poisson manifolds equipped with Hermitian star products. The authors prove that strong and ring-theoretic Morita equivalence induce the same equivalence relation but in general different Picard groups. Finally, the authors consider star products and show how the difference mentioned above can be interpreted in this case via cohomological terms.

MSC:

 53D55 Deformation quantization, star products 53D10 Contact manifolds (general theory)
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