English

Maximal amenable MASAs of radial type in the free group factors

Operator Algebras 2023-02-28 v1

Abstract

We prove that if {(Mj,τj)}jJ\{(M_j, \tau_j)\}_{j\in J} are tracial von Neumann algebras, sjMjs_j \in M_j are selfadjoint semicircular elements and t=(tj)jt=(t_j)_j is a square summable JJ-tuple of real numbers with at least two non-zero entries, then the von Neumann algebra A(t)A(t) generated by the ``weighted radial element'' jtjsjM:=jJMj\sum_j t_j s_j\in M:=*_{j\in J} M_j is maximal amenable in MM, with A(t)A(t), A(t)A(t') unitary conjugate in MM iff t,tt, t' are proportional. Letting MjM_j be diffuse amenable, j\forall j, this provides a large family of maximal amenable MASAs in the free group factor LFnL\mathbb F_n.

Keywords

Cite

@article{arxiv.2302.13355,
  title  = {Maximal amenable MASAs of radial type in the free group factors},
  author = {Remi Boutonnet and Sorin Popa},
  journal= {arXiv preprint arXiv:2302.13355},
  year   = {2023}
}

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6 pages