LongoRehren subfactors arising from $\alpha$induction
Abstract
We study (dual) LongoRehren subfactors $M\otimes M^{opp} \subset R$ arising from various systems of endomorphisms of M obtained from alphainduction for some braided subfactor $N\subset M$. Our analysis provides useful tools to determine the systems of RR morphisms associated with such LongoRehren subfactors, which constitute the ``quantum double'' systems in an appropriate sense. The key to our analysis is that alphainduction produces halfbraidings in the sense of Izumi, so that his general theory can be applied. Nevertheless, alphainduced systems are in general not braided, and thus our results allow to compute the quantum doubles of (certain) systems without braiding. We illustrate our general results by several examples, including the computation of the quantum double systems for the asymptotic inclusion of the E_8 subfactor as well as its three analogues arising from conformal inclusions of SU(3)_k.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:math/0002154
 Bibcode:
 2000math......2154B
 Keywords:

 Operator Algebras;
 Mathematical Physics;
 Quantum Algebra;
 46L37 (Primary) 81T40;
 81T05 (Secondary)
 EPrint:
 31 pages, latex