Journal of Operator Theory
Volume 86, Issue 1, Summer 2021 pp. 145-161.
Commuting squares and planar subalgebras
Authors:
Keshab Chandra Bakshi (1), Vijay Kodiyalam (2)
Author institution: (1) Chennai Mathematical Institute, Chennai, India
(2) The Institute of Mathematical Sciences, Chennai, India and Homi Bhabha National Institute, Mumbai, India
Summary: We show a close relationship between non-degenerate smooth commuting squares
of II$_1$-factors with
horizontal inclusions of finite index
and inclusions of subfactor planar
algebras by showing that each leads to a construction of the other.
One direction of this uses the Guionnet--Jones--Shlyakhtenko construction.
DOI: http://dx.doi.org/10.7900/jot.2020feb06.2279
Keywords: Guionnet-Jones-Shlyakhtenko construction, commuting square, subfactor, planar algebra
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