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

TL;DR

This paper demonstrates that the generator subalgebra in $q$-Gaussian von Neumann algebras is maximally amenable for small enough |q|, providing explicit examples and a structural theorem.

Contribution

It introduces explicit examples of maximal amenable subalgebras in $q$-Gaussian algebras and develops a structural theorem for these algebras.

Findings

Generator subalgebra is maximal amenable for small |q|

Constructs a Riesz basis in the spirit of Rulescu

Develops a structural theorem for $q$-Gaussian algebras

Abstract

In this article, we give explicit examples of maximal amenable subalgebras of the $q$-Gaussian algebras, namely, the generator subalgebra is maximal amenable inside the $q$-Gaussian algebras for real numbers $q$ with its absolute value sufficiently small. To achieve this, we construct a Riesz basis in the spirit of R\u{a}dulescu and develop a structural theorem for the $q$-Gaussian algebras.