A PLANAR ALGEBRA CONSTRUCTION OF THE HAAGERUP SUBFACTOR
By E. Peters. 2009
71 citations recorded by the source corpus.
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, that is contained inside a graph planar algebra.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/358562a872747221da0c6743cdd9257804bdec88
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In Algebra and Number Theory
In Geometry and Topology
- Noah Snyder
- S. Morrison
- Vaughan F. R. Jones
- E. Peters
- Zhengwei Liu
- David Penneys
- David E. V. Rose
- Bob Coecke
In Mathematical Physics
- Noah Snyder
- S. Morrison
- Vaughan F. R. Jones
- E. Peters
- Zhengwei Liu
- David Penneys
- David E. V. Rose
- Bob Coecke
Citations in the corpus
- Quadratic Tangles in Planar Algebras (2010, background): “It was one of the contributing factors to a project to classify all subfactors of index ≤ 5 which involves several people including Bigelow, Morrison, Peters and Snyder (see [18],[2]).”
- Skein theory for the D_2pi planar algebras (2008, background): “Other examples of planar algebras which have been described or constructed by generators and relations include the BMW and Hecke algebras [3, 13], the Haagerup subfactor [14], and the Bisch-Haagerup subfactors [15, 16].”
- The classification of subfactors of index at most 5 (2013, methodology): “BMPS12] gave a construction of a long suspected [Ike98] missing case: the extended Haagerup subfactor. This construction roughly follows the outline of Peters’s construction of the Haagerup subfactor [Pet10], but with the addition of a key new idea. Both constructions are based on foundational work ”