A three-functor formalism for commutative von Neumann algebras

Fuente: arXiv
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Main Authors: Henriques, Andre G., Wasserman, Thomas A.
Format: Preprint
Published: 2025
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author Henriques, Andre G.
Wasserman, Thomas A.
author_facet Henriques, Andre G.
Wasserman, Thomas A.
contents A three-functor formalism is the half of a six-functor formalism that supports the projection and base change formulas. In this paper, we provide a three-functor formalism for commutative von Neumann algebras and their modules. Using the Gelfand-Naimark theorem, this gives rise to a three-functor formalism for measure spaces and measurable bundles of Hilbert spaces. We use this to prove Fell absorption for unitary representations of measure groupoids. The three-functor formalism for commutative von Neumann algebras takes values in W*-categories, and we discuss in what sense it is a unitary three-functor formalism.
format Preprint
id arxiv_https___arxiv_org_abs_2504_10131
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A three-functor formalism for commutative von Neumann algebras
Henriques, Andre G.
Wasserman, Thomas A.
Operator Algebras
Category Theory
Quantum Algebra
46L10, 18D40
A three-functor formalism is the half of a six-functor formalism that supports the projection and base change formulas. In this paper, we provide a three-functor formalism for commutative von Neumann algebras and their modules. Using the Gelfand-Naimark theorem, this gives rise to a three-functor formalism for measure spaces and measurable bundles of Hilbert spaces. We use this to prove Fell absorption for unitary representations of measure groupoids. The three-functor formalism for commutative von Neumann algebras takes values in W*-categories, and we discuss in what sense it is a unitary three-functor formalism.
title A three-functor formalism for commutative von Neumann algebras
topic Operator Algebras
Category Theory
Quantum Algebra
46L10, 18D40
url https://arxiv.org/abs/2504.10131