Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 5 (2019), 1295-1324.

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

Yusuke Isono

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Let G be a free (unitary or orthogonal) quantum group. We prove that for any nonamenable subfactor NL(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 ̂.

Article information

Anal. PDE, Volume 12, Number 5 (2019), 1295-1324.

Received: 11 January 2018
Accepted: 16 September 2018
First available in Project Euclid: 5 January 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L10: General theory of von Neumann algebras 46L36: Classification of factors
Secondary: 58B32: Geometry of quantum groups

von Neumann algebra type III factor Cartan subalgebra


Isono, Yusuke. Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors. Anal. PDE 12 (2019), no. 5, 1295--1324. doi:10.2140/apde.2019.12.1295.

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