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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.

Keywords: Guionnet-Jones-Shlyakhtenko construction, commuting square, subfactor, planar algebra

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