On the non-occurrence of the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) as the principal graph of an inclusion of II\(_ 1\) factors (Q1318505)
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scientific article; zbMATH DE number 540681
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the non-occurrence of the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) as the principal graph of an inclusion of II\(_ 1\) factors |
scientific article; zbMATH DE number 540681 |
Statements
On the non-occurrence of the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) as the principal graph of an inclusion of II\(_ 1\) factors (English)
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27 April 1994
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After discussing some preliminaries on the notion of an action of a hypergroup on a set, we present elementary proofs of the fact that the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) do not arise as Jones' principal graph invariant of an inclusion of \(\Pi_ 1\) factors. (Here, we use the symbol \(\beta_ n\) to denote the graph that is normally denoted by \(B_ n\), the reason for this changed terminology being spelt out in the text).
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hypergroup action
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Coxeter graphs
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Jones' principal graph invariant
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\(\Pi_ 1\) factors
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