Constructing the extended Haagerup planar algebra

Constructing the extended Haagerup planar algebra by

Constructing the extended Haagerup planar algebra

We construct a subfactor planar algebra, and as a corollary a subfactor, with the ‘extended Haagerup’ principal graph pair. This is the last open case from Haagerup’s 1993 list of potential principal graphs of subfactors with index in the range (4, 3 + √ 3) . We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a descriptio...

A Planar Algebra Construction of the Haagerup Subfactor

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 o...

On Constructing Resolutions over the Polynomial Algebra

Let k be a field, and A be a polynomial algebra over k. Let I ⊆ A be an ideal. We present a novel method for computing resolutions of A/I over A. The method is a synthesis of Gröbner basis techniques and homological perturbation theory. The examples in this paper were computed using computer algebra. To Jan–Erik Roos on his sixty–fifth birthday Appears in Homology, Homotopy and Applications, vo...

Constructing Prime-field Planar Configurations

An infinite class of planar configurations is constructed with distinct prime-field characteristic sets (i.e., configurations represented over a finite set of prime fields but over fields of no other characteristic). It is shown that if p is sufficiently large, then every subset of k primes between p and f(p, k) forms such a set (where f(p, k) = 2[(f-Ak3//2)Bk3/21 for constants A and B). In par...