Subfactors from braided C∗tensor categories

Abstract

We extend subfactor constructions originally defined for unitary braid representations to the setting of braided C -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. It was noted by Vaughan Jones that his examples of subfactors gave rise to unitary braid representations. By this we mean representations of the infinite braid group B1 defined by infinitely many generators 1; 2;::: which satisfy the familiar braid relations. Subsequently, unitary braid representations were used by A. Ocneanu and by H. Wenzl to construct new examples of subfactors; here the subfactor is given by the subgroup B2;1 generated by 2; 3;::: . This construction was denoted as the one-sided subfactor construction by J. Erlijman, as opposed to her multisided subfactors. Here, for a given integer s > 1, the s-sided subfactor is obtained as a suitable inductive limit of the embeddings of the quotients of B s D Bn