A2-planar algebras I

Evans, David Emrys and Pugh, Mathew J. ORCID: https://orcid.org/0000-0001-9045-3713 2010. A2-planar algebras I. Quantum Topology 1 (4) , pp. 321-377. 10.4171/QT/8

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Abstract

We give a diagrammatic presentation of the A2-Temperley–Lieb algebra. Generalizing Jones’ notion of a planar algebra, we formulate an A2-planar algebra motivated by Kuperberg’s A2-spider. This A2-planar algebra contains a subfamily of vector spaces which will capture the double complex structure pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system, including both the periodicity three coming from the A2-Temperley–Lieb algebra as well as the periodicity two coming from the subfactor basic construction. We use an A2-planar algebra to obtain a description of the (Jones) planar algebra for the Wenzl subfactor in terms of generators and relations.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Subfactors, planar algebras, SU(3)
Publisher:	European Mathematical Society
ISSN:	1663-487X
Date of First Compliant Deposit:	30 March 2016
Last Modified:	17 May 2023 07:12
URI:	https://orca.cardiff.ac.uk/id/eprint/26501

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