A2-Planar Algebras II: Planar Modules
arXiv:0906.4311
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.
33 pages, 19 figures; revised definition of A_2-planar modules, improvements to exposition and introduction
References in corpus (8)
- Random matrices, free probability, planar algebras and subfactors
- Skein theory for the D_{2n} planar algebras
- Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs
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- The planar algebra of diagonal subfactors
- The planar algebra of group-type subfactors
- From subfactor planar algebras to subfactors
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