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A few remarks on Pimsner–Popa bases and regular subfactors of depth 2

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  01 December 2021

Keshab Chandra Bakshi  and
Ved Prakash Gupta
Keshab Chandra Bakshi
Affiliation:
Chennai Mathematical Institute, Chennai, India. e-mail: bakshi209@gmail.com
Ved Prakash Gupta
Affiliation:
School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India
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Abstract

We prove that a finite index regular inclusion of $II_1$ -factors with commutative first relative commutant is always a crossed product subfactor with respect to a minimal action of a biconnected weak Kac algebra. Prior to this, we prove that every finite index inclusion of $II_1$ -factors which is of depth 2 and has simple first relative commutant (respectively, is regular and has commutative or simple first relative commutant) admits a two-sided Pimsner–Popa basis (respectively, a unitary orthonormal basis).

Keywords

Pimsner-Popa basesweak Hopf algebraregular subfactorunitary basisJones index

MSC classification

Primary: 46L37: Subfactors and their classification
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 3 , September 2022 , pp. 586 - 602
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

In memory of Vaughan Jones, a true pioneer!

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