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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Examples of factors which have no Cartan subalgebras


Author: Yusuke Isono
Journal: Trans. Amer. Math. Soc. 367 (2015), 7917-7937
MSC (2010): Primary 20G42, 46L10
DOI: https://doi.org/10.1090/tran/6321
Published electronically: April 24, 2015
MathSciNet review: 3391904
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Abstract: 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 $ \rm 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.


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Additional Information

Yusuke Isono
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan
Address at time of publication: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: isono@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/tran/6321
Received by editor(s): October 10, 2012
Received by editor(s) in revised form: November 23, 2012, March 13, 2013, June 23, 2013, and August 16, 2013
Published electronically: April 24, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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