The pop-switch planar algebra and the Jones-Wenzl idempotents

2015/01/19 by Ellie Grano, Grano, Ellie, Stephen Bigelow +1
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.GN #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1501.04672

arxiv created 2015/01/19 · arxiv updated 2015/01/21

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 A_n. In the tensor category of idempotents of the pop-switch planar algebra, the nth Jones-Wenzl idempotent is isomorphic to a direct sum of n+1 diagrams consisting of only vertical strands.

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