2003/09/24 by Henrique Bursztyn, Stefan Waldmann, Bursztyn, Henrique +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA
paper · pdf · doi:10.48550/arxiv.math/0309402
30 pages, shortened/revised version to appear in Pacific. J. Math (the appendix has been removed)
openalex publication_date 2003/09/24 · arxiv created 2004/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.