A(2)-planar algebras II: Planar modules

Evans, David E. and Pugh, Mathew J. ORCID: https://orcid.org/0000-0001-9045-3713 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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Abstract

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
URI:	https://orca.cardiff.ac.uk/id/eprint/11932

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