Index for factors generated by extended Jones' projections
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.
scientific article; zbMATH DE number 633566