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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the symmetric enveloping algebra of planar algebra subfactors


Authors: Stephen Curran, Vaughan F. R. Jones and Dimitri Shlyakhtenko
Journal: Trans. Amer. Math. Soc. 366 (2014), 113-133
MSC (2010): Primary 46L37, 46L54
Published electronically: September 19, 2013
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Abstract: We give a diagrammatic description of Popa's symmetric enveloping algebras associated to planar algebra subfactors. As an application we construct a natural family of derivations on these factors and compute a certain free entropy dimension type quantity.


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Additional Information

Stephen Curran
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095
Address at time of publication: The D. E. Shaw Group, New York, New York 10036
Email: curransr@math.ucla.edu, Stephen.Curran@deshaw.com

Vaughan F. R. Jones
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: vfr@math.berkeley.edu

Dimitri Shlyakhtenko
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095
Email: shlyakht@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05910-7
PII: S 0002-9947(2013)05910-7
Received by editor(s): October 3, 2011
Published electronically: September 19, 2013
Additional Notes: The first author’s research was supported by an NSF postdoctoral fellowship and NSF grant DMS-0900776.
The second author’s research was supported by NSF grant DMS-0856316.
The third author’s research was supported by NSF grant DMS-0900776
All the authors were also supported by DARPA Award 0011-11-0001.
Article copyright: © Copyright 2013 American Mathematical Society