Index for factors generated by extended Jones' projections
type: Item
instance of: scholarly article
title: Index for factors generated by extended Jones' projections
zbMATH Open document ID: 0822.46075
author: Atsushi Sakuramoto
published in: Journal of Mathematics of Kyoto University
publication date: 1994-09-05T00:00:00Z
review text: In [Invent. Math. 72, 1-25 (1983; Zbl 0508.46040)], \textit{V. F. R. Jones} studied families \(\{e_ i \}_{i\in \mathbb{N}}\) of projections satisfying certain conditions depending on a single real parameter. In the current paper, the author imposes similar conditions on a family indexed as \(\{e_ i \}_{n\in \mathbb{N}}\cup \{f_ j\}_{1\leq j\leq\ell}\) and depending on several real parameters. Feasible values for the parameters are determined. Writing \(B\) for the von Neumann algebra generated by the \(\{e_ i\}\) and \(A\) for the von Neumann algebra generated by \(B\) and the \(\{f_ j\}\), the author then evaluates the index \([A:B]\) whenever it exists.
Mathematics Subject Classification ID: 46L37
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 633566
zbMATH Keywords: index for factors
zbMATH Keywords: extended Jones' projections
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: index
reviewed by: Edward A. Azoff
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519071
OpenAlex ID: W1555816567
DOI: 10.1215/KJM/1250519071
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description: scientific article; zbMATH DE number 633566