Comptes Rendus
Research article - Functional analysis
Factoriality of twisted locally compact group von Neumann algebras
Stefaan Vaes1 
1 Department of Mathematics, KU Leuven, Belgium
Comptes Rendus. Mathématique, Volume 363 (2025), pp. 853-859

We construct an exotic example of a locally compact group $\mathcal{G}$ with a Borel $2$-cocycle $\omega $ such that the non-twisted group von Neumann algebra $L(\mathcal{G})$ is a factor, while the twisted group von Neumann algebra $L_\omega (\mathcal{G})$ has a diffuse center.

Nous construisons un exemple exotique d’un groupe localement compact $\mathcal{G}$ avec un $2$-cocycle borélien $\omega $ tels que l’algèbre de von Neumann non-twistée $L(\mathcal{G})$ est un facteur, tandis que l’algèbre de von Neumann twistée $L_\omega (\mathcal{G})$ a un centre diffus.

Received:
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Accepted:
Published online:
DOI: 10.5802/crmath.769
Classification: 46L10
Keywords: Group von Neumann algebra, factoriality, scalar $2$-cocycle, cocycle twisted group von Neumann algebra
Mots-clés : Algèbre de von Neumann d’un groupe, factorialité, $2$-cocycle scalaire, algèbre de von Neumann twistée d’un groupe

Stefaan Vaes 1

1 Department of Mathematics, KU Leuven, Belgium
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Factoriality of twisted locally compact group von {Neumann} algebras},
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Stefaan Vaes. Factoriality of twisted locally compact group von Neumann algebras. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 853-859. doi: 10.5802/crmath.769

[1] K. De Commer; J. Krajczok Braided tensor product of von Neumann algebras | arXiv

[2] Adam Kleppner The structure of some induced representations, Duke Math. J., Volume 29 (1962), pp. 555-572 | Zbl

[3] S. M. Srivastava Selection and representation theorems for σ-compact valued multifunctions, Proc. Am. Math. Soc., Volume 83 (1981), pp. 775-780 | Zbl

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