Vol. 12, No. 5, 2019

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

Yusuke Isono

Vol. 12 (2019), No. 5, 1295–1324
Abstract

Let G be a free (unitary or orthogonal) quantum group. We prove that for any nonamenable subfactor N L(G) which is an image of a faithful normal conditional expectation, and for any σ-finite factor B, the tensor product N¯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(G)¯B as the one relative to B, by using an operator-valued weight to B and the central weak amenability of G ̂.

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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