Examples of factors which have no Cartan subalgebras
By Yusuke Isono. 2012
49 citations recorded by the source corpus.
We consider some conditions similar to Ozawa's condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a corollary, we prove that $\rm II_1$ factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type $\rm III_1$ factors with such a condition are semisolid as a $\rm II_\infty$ factor.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/303def16de7fc36b7c06417ee98b347648fb1bd8
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In Algebra and Number Theory
- Makoto Yamashita
- Michael Brannan
- Amaury Freslon
- K. De Commer
- Benoît Collins
- Roland Vergnioux
- Roland Speicher
- Moritz Weber
In Applied Mathematics
In Mathematical Physics
- Amaury Freslon
- Michael Brannan
- Makoto Yamashita
- K. De Commer
- Benoît Collins
- Roland Vergnioux
- Roland Speicher
- T. Banica
Citations in the corpus
- The Connes embedding property for quantum group von Neumann algebras (2014, background): “These connections occur at the lev l of quantum symmetries and asymptotic freeness results [3, 6, 10, 17, 18], and also at th e operator algebra level [9, 19, 21, 22, 23, 35].”
- CCAP for Universal Discrete Quantum Groups (2013, background): “Regarding FOF , recent work of Isono [23] on a strengthened Akemann–Ostrand property established that the von Neumann algebra L(FOF ) has no Cartan subalgebra provided it has the W ∗CCAP and is not injective.”
- Reduced operator algebras of trace-preserving quantum automorphism groups (2012, methodology): “Using the terminology of Isono [25], Theorem 5.”