arXiv subjects
Publications and source records attributed to Chenxu Wen.
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 Rădulescu and develop a structural theorem for the $q$-Gaussian algebras.
Given $-1 < q < 1$ and a separable real Hilbert space with dimension no less than 2, we prove that the generator subalgebra in the $q$-Gaussian algebra is singular.
Consider an inclusion of diffuse von Neumann algebras A c M . We say that A c M has the absorbing amenability property if for any diffuse subalgebra B c A and any amenable intermediate algebra B c D c M we have that D is contained in A. We prove that the cup subalgebra associated to any subfactor planar algebra has the absorbing amenability property.
We prove that the radial masa C in the free group factor is disjoint from other maximal amenable subalgebras in the following sense: any distinct maximal amenable subalgebra cannot have diffuse intersection with C.