Bicategories of operator algebras and Poisson manifolds

2000/08/02 by N.P. Landsman, N. P. Landsman, Landsman, N. P. · 1 citation
Mathematics · Physics and Astronomy · #18D05 #22A22 #46L08 #53D17 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Symplectic Geometry (math.SG) #math-ph #math.CT #math.MP #math.OA #math.SG #msc:18D05 #msc:22A22 #msc:46L08 #msc:53D17

paper · pdf · doi:10.48550/arxiv.math-ph/0008003

15 pages. Style file updated (refs. were not numbered)

openalex publication_date 2000/08/02 · arxiv created 2000/08/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that rings are the objects of a bicategory, whose arrows are bimodules, composed through the bimodule tensor product. We give an analogous bicategorical description of C*-algebras, von Neumann algebras, Lie groupoids, symplectic groupoids, and Poisson manifolds. The upshot is that known definitions of Morita equivalence for any of these cases amount to isomorphism of objects in the pertinent bicategory.

Citations

• Morita equivalence for c∗-algebras and w∗-algebras

Cited by

• Bicategories of C*-correspondences as Dwyer-Kan localisations

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