Non-Semisimple Planar Algebras from the Representation Theory of U_q(\mathfraksl₂)

2017/03/31 by Stephen Moore · 1 citation
Mathematics · #math.OA #math.QA #math.RT

paper · pdf · doi:10.1142/s0129055x18500174

21 pages, 28 figures

arxiv created 2018/08/12 · arxiv updated 2018/08/14

Abstract

We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group U_q(\mathfraksl₂). This is a diagrammatic description of End_U_q(\mathfraksl₂)(X^{⊗ n}), where X:=X⁺₂ is a two dimensional U_q(\mathfraksl₂) module.

Cited by

• Diagrammatic morphisms between indecomposable modules of U_q(\mathfraksl₂)

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