Diagrammatic Construction of Representations of Small Quantum ${\mathfrak{sl}}_2$

Abstract

We provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of ${\mathfrak{sl}}_2$ at a root of unity $q$ of odd order. Our approach is diagrammatic, and it relies on an extension of the Temperley-Lieb category specialized at $\delta =-q-q^{-1}$.

37 pages, proofs and references expanded in version 3

References in corpus (2)

• Mapping Class Group Representations From Non-Semisimple TQFTs
• Non-Semisimple 3-Manifold Invariants Derived From the Kauffman Bracket

Cited by in corpus (1)

• Non-Semisimple 3-Manifold Invariants Derived From the Kauffman Bracket