Mixed -deformed Araki–Woods von Neumann algebras

  • Panchugopal Bikram

    National Institute of Science Education and Research, Jatni, India
  • Rahul Kumar R

    Indian Institute of Technology Madras, Chennai, India
  • Kunal Mukherjee

    Indian Institute of Technology Madras, Chennai, India
Mixed $q$-deformed Araki–Woods von Neumann algebras cover
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Given a strongly continuous orthogonal representation of on a real Hilbert space , a decomposition consisting of invariant subspaces of and an appropriate matrix of real parameters, we associate representations of the mixed commutation relations on twisted Fock spaces. The associated von Neumann algebras are (usually) non-tracial and are generalizations of those constructed by Bożejko–Speicher and Hiai. We investigate the factoriality of these von Neumann algebras. Along the process, we show that the generating abelian subalgebras associated with the blocks of the aforesaid decomposition are strongly mixing masas when they admit appropriate conditional expectations. On the contrary, the generating abelian algebras which fail to admit appropriate conditional expectations are quasi-split. We also discuss non-injectivity and the Haagerup approximation property.

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Panchugopal Bikram, Rahul Kumar R, Kunal Mukherjee, Mixed -deformed Araki–Woods von Neumann algebras. J. Noncommut. Geom. 17 (2023), no. 4, pp. 1231–1297

DOI 10.4171/JNCG/513