On the Structure of Graph Product von Neumann Algebras
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.
Authors
- Rolando de Santiago (ORCID: https://orcid.org/0000-0003-2353-9116)
- Srivatsav Kunnawalkam Elayavalli (ORCID: https://orcid.org/0000-0002-7928-2068)
- David Jekel (ORCID: https://orcid.org/0000-0002-8580-5064)
- Ian Charlesworth (ORCID: https://orcid.org/0000-0003-0546-2856)
- Ben Hayes (ORCID: https://orcid.org/0000-0001-9759-7672)
- Brent Nelson (ORCID: https://orcid.org/0000-0002-8388-3018)
Institutions
- University of Copenhagen (DK)
- University of California San Diego (US)
- University of Virginia (US)
- California State University, Long Beach (US)
- Cardiff Metropolitan University (GB)
- Michigan State University (US)
Publication Details
- Journal
- Publications of the Research Institute for Mathematical Sciences
- Published
- 2025-10-22
- DOI
- https://doi.org/10.4171/prims/61-4-3
- Citations
- 1
- Primary Topic
- Advanced Operator Algebra Research
- Type
- article
- Field-Weighted Citation Impact
- 3.69
Funders
- National Science Foundation
- American Institute of Mathematics
- Natural Sciences and Engineering Research Council of Canada