Maximal amenable MASAs of radial type in the free group factors

2023/02/26 by Boutonnet, Remi, Popa, Sorin · 1 citation
#46L10 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2302.13355

Abstract

We prove that if \(M_j, τ_j)\_{j∈ J} are tracial von Neumann algebras, s_j ∈ M_j are selfadjoint semicircular elements and t=(t_j)_j is a square summable J-tuple of real numbers with at least two non-zero entries, then the von Neumann algebra A(t) generated by the ``weighted radial element'' ∑_j t_j s_j∈ M:=*_{j∈ J} M_j is maximal amenable in M, with A(t), A(t') unitary conjugate in M iff t, t' are proportional. Letting M_j be diffuse amenable, ∀ j, this provides a large family of maximal amenable MASAs in the free group factor L\mathbb F_n.

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• Compressible subalgebras in II₁ factors

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