Maximal amenability of the generator subalgebra in q-Gaussian von Neumann algebras

Parekh, Sandeepan; Shimada, Koichi; Wen, Chenxu

doi:10.7900/jot.2017jun28.2167

Cited by 6 publications

(4 citation statements)

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“…[37,95] respectively that the generator MASA and the radial MASA admit the absorbing amenability property. This work inspired many papers establishing the absorbing amenability property (and other absorption properties such as Gamma stability) in many examples (see [8,36,61]).…”

Section: Introductionmentioning

confidence: 82%

“…This answered in the negative a question of Kadison at the 1967 Baton Rouge conference who asked if every self-adjoint operator in a II 1 -factor is contained in a hyperfinite subfactor. The technique of asymptotic orthogonality developed by Popa to achieve the above result has been used successfully to establish this maximal amenability property for various natural subalgebras of the free group factors, such as the radial MASA [9] (see also [8,61]). Recently Boutonnet and Popa also construct a continuum size family (M α ) α ) of interesting maximally amenable subalgebras [6] in any free product of diffuse tracial von Neumann algebras (in particular for free group factors) with the property that M α is not unitarily conjugate to M β if α = β.…”

Section: Introductionmentioning

confidence: 99%

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A random matrix approach to the Peterson-Thom conjecture

Hayes¹

2022

Indiana Univ. Math. J.

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In this paper we show various new structural properties of free group factors using the recent resolution (due independently to Belinschi-Capitaine and Bordenave-Collins) of the Peterson-Thom conjecture. These results include the resolution to the coarseness conjecture independently due to the first-named author and Popa, a generalization of Ozawa-Popa's celebrated strong solidity result using vastly more general versions of the normalizer (and in an ultraproduct setting), a dichotomy result for intertwining of maximal amenable subalgebras of interpolated free group factors, as well as application to ultraproduct embeddings of nonamenable subalgebras of interpolated free group factors.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

A random matrix approach to the Peterson-Thom conjecture

Hayes¹

2022

Indiana Univ. Math. J.

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“…For many examples of maximal amenable subalgebras of free group factors this has been verified [74,9,55], and typically uses a generalization of Popa's asymptotic orthogonality property, called the strong asymptotic orthogonality property implicitly defined in [36,Theorem 3.1]. Many exciting recent works [6,52,7] apply an alternative method using an analysis of states.…”

Section: Introductionmentioning

confidence: 99%

A random matrix approach to the Peterson-Thom conjecture

Hayes¹

2020

Preprint

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The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on L 2 -Betti numbers. We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjørnsen theorem whose validity would imply the Peterson-Thom conjecture. This random matrix conjecture is related to recent work of .

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“…For example, in [Hou15] Houdayer defined a generalization of Popa's asymptotic orthogonal property now called the strong asymptotic orthogonality property from which one can deduce an amenable absorption property: if Q ≤ M is amenable and Q ∩ A is diffuse, then Q ⊆ A. This strengthening of the asymptotic orthogonality property was then used in [Wen16,BW16,PSW18] to give other examples of situations where one has amenable absorption for maximal amenable subalgebras of free group factors. We remark in passing that it is a conjecture of Peterson and Thom (see the discussion following [PT11, Proposition 7.7]) that every maximal amenable subalgebra of a free group factor has the amenable absorption property.…”

Section: Introductionmentioning

confidence: 99%

A random matrix approach to absorption in free products

Hayes

Jekel

Nelson

et al. 2019

Preprint

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This paper gives a free entropy theoretic perspective on amenable absorption results for free products of tracial von Neumann algebras. In particular, we give the first free entropy proof of Popa's famous result that the generator MASA in a free group factor is maximal amenable, and we partially recover Houdayer's results on amenable absorption and Gamma stability. Moreover, we give a unified approach to all these results using 1-bounded entropy. We show that if M = P * Q, then P absorbs any subalgebra of M that intersects it diffusely and that has 1-bounded entropy zero (which includes amenable and property Gamma algebras as well as many others). In fact, for a subalgebra P ≤ M to have this absorption property, it suffices for M to admit random matrix models that have exponential concentration of measure and that "simulate" the conditional expectation onto P.

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Maximal amenability of the generator subalgebra in q-Gaussian von Neumann algebras

Cited by 6 publications

References 28 publications

A random matrix approach to the Peterson-Thom conjecture

A random matrix approach to the Peterson-Thom conjecture

A random matrix approach to the Peterson-Thom conjecture

A random matrix approach to absorption in free products

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