Let be a free (unitary or orthogonal) quantum group. We prove that for any nonamenable subfactor which is an image of a faithful normal conditional expectation, and for any -finite factor , the tensor product has no Cartan subalgebras. This generalizes our previous work that provides the same result when is finite. In the proof, we establish Ozawa–Popa and Popa–Vaes’s weakly compact action on the continuous core of as the one relative to , by using an operator-valued weight to and the central weak amenability of .
"Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors." Anal. PDE 12 (5) 1295 - 1324, 2019. https://doi.org/10.2140/apde.2019.12.1295