Cartan subalgebras in W*-algebras
arxiv(2024)
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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