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    • Keywords


      von Neumann algebras associated to graphs; Guionnet–Jones–Shlya-khtenko construction (for possibly non-bipartite graphs); free Poisson variable.

    • Abstract


      We investigate a construction (from Kodiyalam Vijay and Sunder V S, J. Funct. Anal.260 (2011) 2635–2673) which associates a finite von Neumann algebra $M(\Gamma, \mu)$ to a finite weighted graph $(\Gamma, \mu)$. Pleasantly, but not surprisingly, the von Neumann algebra associated to a `flower with 𝑛 petals’ is the group on Neumann algebra of the free group on 𝑛 generators. In general, the algebra $M(\Gamma, \mu)$ is a free product, with amalgamation over a finite-dimensional abelian subalgebra corresponding to the vertex set, of algebras associated to subgraphs `with one edge’ (or actually a pair of dual edges). This also yields `natural’ examples of (i) a Fock-type model of an operator with a free Poisson distribution; and (ii) $\mathbb{C}\oplus\mathbb{C}$-valued circular and semi-circular operators.

    • Author Affiliations


      Madhushree Basu1 Vijay Kodiyalam1 V S Sunder1

      1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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