Non-Semisimple Planar Algebras from the Representation Theory of ${\bar{U}}_q({\mathfrak{sl}}_2)$

Abstract

We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group ${\bar{U}}_q({\mathfrak{sl}}_2)$. This is a diagrammatic description of $En{d}_{{\bar{U}}_q({\mathfrak{sl}}_2)}(X^{\otimes n})$, where $X:={\mathcal{X}}_2^{+}$ is a two dimensional ${\bar{U}}_q({\mathfrak{sl}}_2)$ module.

21 pages, 28 figures

References in corpus (1)

• Lattice W-algebras and logarithmic CFTs

Cited by in corpus (2)

• Diagrammatic morphisms between indecomposable modules of ${\bar{U}}_q({\mathfrak{sl}}_2)$
• Diagrammatic Construction of Representations of Small Quantum ${\mathfrak{sl}}_2$