Subfactors from braided $C^*$ tensor categories

Juliana Erlijman and Hans Wenzl

Vol. 231 (2007), No. 2, 361–399

DOI: 10.2140/pjm.2007.231.361

Abstract

We extend subfactor constructions originally defined for unitary braid representations to the setting of braided $C^{\ast }$-tensor categories. The categorical approach is then used to compute the principal graph of these subfactors. We also determine the dual principal graph for several important cases. Here invertibility of the so-called $S$-matrix of a subcategory and certain related group actions play an important role.

Keywords

subfactor, braided $C^*$ tensor category

Mathematical Subject Classification 2000

Primary: 46L37

Secondary: 18D10

Milestones

Received: 23 November 2005

Revised: 28 February 2007

Accepted: 13 March 2007

Published: 1 June 2007