Abstract
It is a wide open problem to give an intrinsic criterion for a factor to admit a Cartan subalgebra . When is a Cartan subalgebra, the -bimodule is simple in the sense that the left and right actions of generate a maximal abelian subalgebra of . A factor that admits such a subalgebra is said to be -thin. Very recently, Popa discovered an intrinsic local criterion for a factor to be -thin and left open the question whether all -thin factors admit a Cartan subalgebra. We answer this question negatively by constructing -thin factors without Cartan subalgebras.
Citation
Anna Sofie Krogager. Stefaan Vaes. "Thin factors with no Cartan subalgebras." Kyoto J. Math. 59 (4) 815 - 867, December 2019. https://doi.org/10.1215/21562261-2019-0028
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