Abstract:We completely classify the atomic summands in a graph product $(M,\varphi) = *_{v \in \mathcal{G}} (M_v,\varphi_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,\psi)$ is a tensor product of type I factor summands $(N_v,\psi_v)$ in the individual algebras. The existence of such a summand and its weight in the direct sum can be determined from the $(N_v,\psi_v)$'s using explicit polynomials associated to the graph.
From: David Jekel [view email]
[v1]
Tue, 10 Jun 2025 17:20:17 UTC (29 KB)
[v2]
Wed, 29 Jul 2026 16:58:15 UTC (39 KB)
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