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arXiv · 2403.17621

Cartan subalgebras in W*-algebras

Jean Renault
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Abstract

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.

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Jean Renault. 2024-03-26. Cartan subalgebras in W*-algebras. https://arxiv.org/abs/2403.17621

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