Completely positive inner products and strong Morita equivalence

Abstract

We develop a general framework for the study of strong Morita equivalence in which $C^{\ast }$-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 ${}^{\ast }$-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.

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

Cited by in corpus (4)

• Poisson geometry and Morita equivalence
• Induction of representations in deformation quantization
• The Covariant Picard Groupoid in Differential Geometry
• The H-Covariant Strong Picard Groupoid