Completely positive inner products and strong Morita equivalence

Details Completely positive inner products and strong Morita equivalence Completely positive inner products and strong Morita equivalence

2003-09-24

arxiv.org/abs/math/0309402v3

Mathematics

Quantum Algebra

30 pages, shortened/revised version to appear in Pacific. J. Math (the appendix has been removed)

Scientific paper

We develop a general framework for the study of strong Morita equivalence in which $C^*$-algebras and hermitian star products on Poisson manifolds are treated in equal footing. We compare strong and ring-theoretic Morita equivalences in terms of their Picard groupoids for a certain class of unital $^*$-algebras encompassing both examples. Within this class, we show that both notions of Morita equivalence induce the same equivalence relation but generally define different Picard groups. For star products, this difference is expressed geometrically in cohomological terms.

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