Publications

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

Published in Journal of Operator Theory, 2018

We develop a structural theorem for the q-Gaussian algebras, namely, we construct a Riesz basis for the q-Fock space in the spirit of Radulescu. As an application, we show that the generator subalgebra is maximal amenable inside the q-Gaussian von Neumann algebra for any real number q with absolute value less than 1/9.

Recommended citation: Parekh S., Shimada K. & Wen, C.(2018). Maximal amenability of the generator subalgebra in *q*-Gaussian von Neumann algebras, Journal of Operator Theory, 80(1), pp. 125-152.
http://www.mathjournals.org/jot/2018-080-001/2018-080-001-007.html

Singularity of the generator subalgebra in q-Gaussian algebras

Published in Proceedings of American Mathematical Society, 2017

We prove that the generator masa in the q-Gaussian factors, where -1<q<1, is always singular.

Recommended citation: Wen, C.(2017). Singularity of the generator subalgebra in *q*-Gaussian algebras, Proceedings of American Mathematical Society, 145(8), pp. 3493-3500.
http://www.ams.org/journals/proc/2017-145-08/S0002-9939-2017-13481-9/S0002-9939-2017-13481-9.pdf

Maximal amenability and disjointness for the radial masa

Published in Journal of Functional Analysis, 2016

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.

Recommended citation: Wen, C.(2016). Maximal amenability and disjointness for the radial masa, Journal of Functional Analysis, 270(2), pp. 787-801.
https://www.sciencedirect.com/science/article/pii/S0022123615003298

Amenable extensions in II1 factors

Published in Vanderbilt University Electronic Theses and Dissertations, 2016

Recommended citation: Wen, C. (2016). Amenable extensions in II1 factors. Retrieved from vVanderbilt University Electronic Theses and Dissertations.
https://etd.library.vanderbilt.edu/available/etd-06152016-134905/unrestricted/Wen.pdf

The cup subalgebra has the absorbing amenability property

Published in International Journal of Mathematics, 2016

Consider an inclusion of diffuse von Neumann algebras A inside M. We say that the inclusion has the absorbing amenability property (AAP) if for any diffuse subalgebra B inside A and any amenable intermediate algebra D between B and M, we have that D is contained in A. We prove that the cup subalgebra associated to any subfactor planar algebra has the AAP.

Recommended citation: Brothier A. & Wen, C.(2016). The cup subalgebra has the absorbing amenability property, International Journal of Mathematics, 27, 1650013.
https://www.worldscientific.com/doi/10.1142/S0129167X16500130