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28 March 2024
 
  » arxiv » math.OA/9810003

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Conformal Nets, Maximal Temperature and Models from Free Probability
C. D’Antoni ; R. Longo ; F. Radulescu ;
Date 1 Oct 1998
Journal J. Operator Theory 45 (2001), no. 1, 195-208
Subject Operator Algebras; Mathematical Physics MSC-class: 46L50 (Primary) 81T05 (Secondary) | math.OA math-ph math.MP
AbstractWe consider conformal nets on $S^1$ of von Neumann algebras, acting on the full Fock space, arising in free probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular structure. The local algebras turn out to be $III_1$-factors associated with free groups. We use our set up to show examples exhibiting arbitrarily large maximal temperatures, but failing to satisfy the split property, then clarifying the relation between the latter property and the trace class conditions on $e^{-L}$, where $L$ is the conformal Hamiltonian.
Source arXiv, math.OA/9810003
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