The Annular Structure of Subfactors
Abstract
Given a planar algebra we show the equivalence of the notions of a module over this algebra (in the operadic sense), and module over a universal annular algebra. We classify such modules, with invariant inner products, in the generic region and give applications to subfactorss, including a planar construction of the $E_6$ and $E_8$ subfactors.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2001
 arXiv:
 arXiv:math/0105071
 Bibcode:
 2001math......5071J
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra;
 46L37;
 57M25
 EPrint:
 62 pages, includes 2 tables and 24 figures, to be published in L'Enseignement Mathematique