Group actions on graphs related to Krishnan-Sunder subfactors

Author:
Bina Bhattacharyya

Journal:
Trans. Amer. Math. Soc. **355** (2003), 433-463

MSC (2000):
Primary 46L37

DOI:
https://doi.org/10.1090/S0002-9947-02-02986-0

Published electronically:
October 8, 2002

MathSciNet review:
1932707

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Abstract | References | Similar Articles | Additional Information

Abstract: We describe the principal graphs of the subfactors studied by Krishnan and Sunder in terms of group actions on Cayley-type graphs. This leads to the construction of a tower of *tree algebras*, for every positive integer , which are symmetries of the Krishnan-Sunder subfactors of index . Using our theory, we prove that the principal graph of the irreducible infinite depth subfactor of index 9 constructed by Krishnan and Sunder is not a tree, contrary to their expectations. We also show that the principal graphs of the Krishnan-Sunder subfactors of index 4 are the affine A and D Coxeter graphs.

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Additional Information

**Bina Bhattacharyya**

Affiliation:
Elance, 820A Kifer Rd., Sunnyvale, California 94086

Email:
Bina_Bhattacharyya_91@post.harvard.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-02986-0

Received by editor(s):
March 8, 1999

Received by editor(s) in revised form:
December 17, 2001

Published electronically:
October 8, 2002

Article copyright:
© Copyright 2002
American Mathematical Society