A2-Planar Algebras II: Planar Modules
نویسندگان
چکیده
Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2-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 A2-planar algebra, and describe certain irreducible Hilbert A2-TL-modules. We construct an A2-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 A2-graph planar algebras is achieved.
منابع مشابه
A 2 -planar Algebras I
We give a diagrammatic representation of the A2-Temperley-Lieb algebra, and show that it is isomorphic to Wenzl’s representation of a Hecke algebra. Generalizing Jones’s notion of a planar algebra, we construct an A2-planar algebra which will capture the structure contained in the SU(3) ADE subfactors. We show that the subfactor for an ADE graph with a flat connection has a description as a fla...
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