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A(2)-planar algebras II: Planar modules

Evans, David E. and Pugh, Mathew J. ORCID: 2011. A(2)-planar algebras II: Planar modules. Journal of Functional Analysis 261 (7) , pp. 1923-1954. 10.1016/j.jfa.2011.05.023

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Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2-planar algebra capturing the structure contained in the double complex per- taining 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 cer- tain 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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Subfactors; Planar algebras; Hilbert planar modules; SU(3)
Publisher: Elsevier
ISSN: 0022-1236
Last Modified: 14 May 2023 13:51

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