A planar algebra construction of the Haagerup subfactor

Details A planar algebra construction of the Haagerup subfactor A planar algebra construction of the Haagerup subfactor

2009-02-08

arxiv.org/abs/0902.1294v2

Mathematics

Operator Algebras

57 pages, added section, fixed typos

Scientific paper

Most known examples of subfactors occur in families, coming from algebraic objects such as groups, quantum groups and rational conformal field theories. The Haagerup subfactor is the smallest index finite-depth subfactor which does not occur in one of these families. In this paper we construct the planar algebra associated to the Haagerup subfactor, which provides a new proof of the existence of the Haagerup subfactor. Our technique is to find the Haagerup planar algebra as a singly generated subfactor planar algebra, contained inside of a graph planar algebra.

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