Sunder, V. S.
(1991)
*On commuting squares and subfactors*
Journal of Functional Analysis, 101
(2).
pp. 286-311.
ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0022-1236(91)90159-3

## 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 1_{R}^{0} of index-values of irreducible subfactors of R, that (N+1/N)^{2} is an accumulation point of 1_{R}^{0}, and that 9 is an accumulation point of accumulation points of 1_{R}^{0}, 16 is an accumulation point of accumulation points of accumulation points of 1_{R}^{0}, and so on.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 53541 |

Deposited On: | 09 Aug 2011 11:50 |

Last Modified: | 09 Aug 2011 11:50 |

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