The atoms of graph product von Neumann algebras

Fuente: arXiv
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Main Authors: Charlesworth, Ian, Jekel, David
Format: Preprint
Published: 2025
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author Charlesworth, Ian
Jekel, David
author_facet Charlesworth, Ian
Jekel, David
contents We completely classify the atomic summands in a graph product $(M,φ) = *_{v \in \mathcal{G}} (M_v,φ_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,ψ)$ is a tensor product of type I factor summands $(N_v,ψ_v)$ in the individual algebras. The existence of such a summand and its weight in the direct sum can be determined from the $(N_v,ψ_v)$'s using explicit polynomials associated to the graph.
format Preprint
id arxiv_https___arxiv_org_abs_2506_09000
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The atoms of graph product von Neumann algebras
Charlesworth, Ian
Jekel, David
Operator Algebras
Probability
46L10, 46L54, 05C25, 05C31
We completely classify the atomic summands in a graph product $(M,φ) = *_{v \in \mathcal{G}} (M_v,φ_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,ψ)$ is a tensor product of type I factor summands $(N_v,ψ_v)$ in the individual algebras. The existence of such a summand and its weight in the direct sum can be determined from the $(N_v,ψ_v)$'s using explicit polynomials associated to the graph.
title The atoms of graph product von Neumann algebras
topic Operator Algebras
Probability
46L10, 46L54, 05C25, 05C31
url https://arxiv.org/abs/2506.09000