The pop-switch planar algebra and the Jones-Wenzl idempotents
Quantum Algebra
2015-01-21 v1 General Topology
Representation Theory
Abstract
The Jones-Wenzl idempotents are elements of the Temperley-Lieb planar algebra that are important, but complicated to write down. We will present a new planar algebra, the pop-switch planar algebra, which contains the Temperley-Lieb planar algebra. It is motivated by Jones' idea of the graph planar algebra of type . In the tensor category of idempotents of the pop-switch planar algebra, the th Jones-Wenzl idempotent is isomorphic to a direct sum of diagrams consisting of only vertical strands.
Keywords
Cite
@article{arxiv.1501.04672,
title = {The pop-switch planar algebra and the Jones-Wenzl idempotents},
author = {Ellie Grano and Stephen Bigelow},
journal= {arXiv preprint arXiv:1501.04672},
year = {2015}
}