A few remarks on Pimsner–Popa bases and regular subfactors of depth 2. (1st September 2022)

• Record Type: Journal Article
• Authors: Bakshi, Keshab Chandra; Gupta, Ved Prakash
• Is Part Of: Glasgow mathematical journal. Volume 64:Part 3(2022)
• Page Start: 586
• Page End: 602
• Publication Date: 2022-09-01
• Subjects: Pimsner-Popa bases -- weak Hopf algebra -- regular subfactor -- unitary basis -- Jones index; 46L37 -- 46L67; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0017089521000379
• Languages: English
• ISSNs: 0017-0895

Abstract

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).