Group actions on graphs related to Krishnan-Sunder subfactors
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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 $k$, which are symmetries of the Krishnan-Sunder subfactors of index $k^2$. 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.References
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Additional Information
- Bina Bhattacharyya
- Affiliation: Elance, 820A Kifer Rd., Sunnyvale, California 94086
- Email: Bina_Bhattacharyya_91@post.harvard.edu
- Received by editor(s): March 8, 1999
- Received by editor(s) in revised form: December 17, 2001
- Published electronically: October 8, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 433-463
- MSC (2000): Primary 46L37
- DOI: https://doi.org/10.1090/S0002-9947-02-02986-0
- MathSciNet review: 1932707