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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A structural result of irreducible inclusions of type $\operatorname {III}_\lambda$ factors, $\lambda \in (0,1)$
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by Phan H. Loi PDF
Proc. Amer. Math. Soc. 126 (1998), 2651-2662 Request permission

Abstract:

Given an irreducible inclusion of factors with finite index $N\subset M$, where $M$ is of type ${III}_{\lambda ^{1/m}}$, $N$ of type ${III}_{\lambda ^{1/n}}$, $0<\lambda <1$, and $m,n$ are relatively prime positive integers, we will prove that if $N\subset M$ satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with $N\subset M$. Relations between $N\subset M$ and a certain $G$-kernel on subfactors are also discussed.
References
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Additional Information
  • Phan H. Loi
  • Affiliation: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435
  • Email: ploi@desire.wright.edu
  • Received by editor(s): June 17, 1996
  • Received by editor(s) in revised form: January 28, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2651-2662
  • MSC (1991): Primary 46L10, 46L55
  • DOI: https://doi.org/10.1090/S0002-9939-98-04349-4
  • MathSciNet review: 1451818