Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors

Isono, Yusuke

doi:10.2140/apde.2019.12.1295

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors

Yusuke Isono

Vol. 12 (2019), No. 5, 1295–1324

DOI: 10.2140/apde.2019.12.1295

Abstract

Let $G$ be a free (unitary or orthogonal) quantum group. We prove that for any nonamenable subfactor $N \subset L^{\infty} (G)$ which is an image of a faithful normal conditional expectation, and for any $σ$ -finite factor $B$ , the tensor product $N \bar{\otimes} B$ has no Cartan subalgebras. This generalizes our previous work that provides the same result when $B$ is finite. In the proof, we establish Ozawa–Popa and Popa–Vaes’s weakly compact action on the continuous core of $L^{\infty} (G) \bar{\otimes} B$ as the one relative to $B$ , by using an operator-valued weight to $B$ and the central weak amenability of $\hat{G}$ .

Keywords

von Neumann algebra, type III factor, Cartan subalgebra

Mathematical Subject Classification 2010

Primary: 46L10, 46L36

Secondary: 58B32

Milestones

Received: 11 January 2018

Accepted: 16 September 2018

Published: 15 December 2018

Authors

Yusuke Isono
Research Institute for Mathematical Sciences Kyoto University Kyoto Japan

Vol. 12, No. 5, 2019