Some remarks on the unrolled quantum group of sl(2)

TL;DR

This paper explores the representation theory of a non-standard quantum deformation of sl(2), providing classifications and morphism descriptions with applications in quantum topology, TQFT, and CFT.

Contribution

It offers new classifications of modules and morphisms for a non-standard quantum sl(2), serving as a survey and foundational reference for related quantum topology research.

Findings

Classification of projective indecomposable modules

Description of morphisms between modules

Connections established with TQFT and CFT

Abstract

In this paper we consider the representation theory of a non-standard quantization of sl(2). This paper contains several results which have applications in quantum topology, including the classification of projective indecomposable modules and a description of morphisms between them. In the process of proving these results the paper acts as a survey of the known representation theory associated to this non-standard quantization of sl(2). The results of this paper are used extensively in [arXiv:1404.7289] to study Topological Quantum Field Theory (TQFT) and have connections with Conformal Field Theory (CFT).