2025/12/15 by Soham Chakraborty, Chakraborty, Soham
Mathematics · #18B40 #37A20 #46L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2512.13878
openalex publication_date 2025/12/15 · openalex created_date 2025/12/18 · openalex updated_date 2026/07/28
It is known to experts that certain regular inclusions of von Neumann algebras arise as crossed products with cocycle actions of the canonical quotient groupoids associated with the inclusions. Similarly, `strongly normal' inclusions of standard equivalence relations arise as semi-direct products with cocycle actions of the quotient groupoids. However, to the author's knowledge, rigorous proofs of these results in full generality are absent in the literature. In this article, we exploit the usual correspondence between inverse semigroups and groupoids, and give a unified approach to proving these `folklore' results and fill this gap in the literature.