A three-functor formalism for commutative von Neumann algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908317984489472 |
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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 |