A2-Planar Algebras II: Planar Modules
Operator Algebras
2011-05-30 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
Abstract
Generalizing Jones's notion of a planar algebra, we have previously introduced an A_2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system. We now introduce the notion of modules over an A_2-planar algebra, and describe certain irreducible Hilbert A_2-TL-modules. We construct an A_2-graph planar algebra associated to each pair (G,W) given by an SU(3) ADE graph G and a cell system W on G. A partial modular decomposition of these A_2-graph planar algebras is achieved.
Cite
@article{arxiv.0906.4311,
title = {A2-Planar Algebras II: Planar Modules},
author = {David E. Evans and Mathew Pugh},
journal= {arXiv preprint arXiv:0906.4311},
year = {2011}
}
Comments
33 pages, 19 figures; revised definition of A_2-planar modules, improvements to exposition and introduction