On the structure of graph product von Neumann algebras

Charlesworth, Ian, De Santiago, Rolando, Hayes, Ben, Jekel, David, Kunnawalkam Elayavalli, Srivatsav and Nelson, Brent 2025. On the structure of graph product von Neumann algebras. Publications of the Research Institute for Mathematical Sciences Item availability restricted.

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Abstract

We undertake a comprehensive study of structural properties of graph products of von Neumann algebras equipped with faithful, normal states, as well as properties of the graph products relative to subalgebras coming from induced subgraphs. Among the technical contributions in this paper is a complete bimodule calculation for subalgebras arising from subgraphs. As an application, we obtain a complete classification of when two subalgebras coming from induced subgraphs can be amenable relative to each other. We also give complete characterizations of when the graph product can be full, diffuse, or a factor. Our results are obtained in a broad generality, and we emphasize that they are new even in the tracial setting. They also allow us to deduce new results about when graph products of groups can be amenable relative to each other.

Item Type:	Article
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	EMS Press
ISSN:	0034-5318
Date of First Compliant Deposit:	16 September 2025
Date of Acceptance:	29 July 2025
Last Modified:	17 Sep 2025 14:45
URI:	https://orca.cardiff.ac.uk/id/eprint/181113

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