# On commuting squares and subfactors

- Authors
- Journal
- Journal of Functional Analysis 0022-1236
- Publisher
- Elsevier
- Publication Date
- Volume
- 101
- Issue
- 2
- Identifiers
- DOI: 10.1016/0022-1236(91)90159-3

## Abstract

Abstract After showing (see Theorem 2.8) how commuting squares lead, in the presence of a certain additional “rotational symmetry” condition, to irreducible subfactors, with pleasant additional features, of the hyperfinite II 1 factor R, it is shown (see Theorem 3.1) that such rotationally symmetric commuting squares can be constructed, starting from each member of a certain class of symmetric non-negative integral matrices. Specialisations of the matrix show (see Sect. 4), for instance, that for each positive integer N, (N + √N 2 + 4) 2 and (N + √N 2 + 8) 2 belong to the set I R 0 of index-values of irreducible subfactors of R, that (N + 1 N ) 2 is an accumulation point of I R 0, and that 9 is an accumulation point of accumulation points of I R 0, 16 is an accumulation point of accumulation points of accumulation points of I R 0, and so on.

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