2024/03/26 by Jean Renault, Renault, Jean
Mathematics · #37D35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2403.17621
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article presents a proof of the Feldman-Moore theorem on Cartan subalgebras in W*-algebras based on the non-commutative Stone equivalence between Boolean inverse semigroups and Boolean groupoids. The proof is decomposed into two parts. The first part writes the W*-algebra as the W*-algebra of the Weyl twist of the Cartan subalgebra. The second part is an extension to separable measure inverse semigroups of the realization of a separable measure algebra by a standard measure space.