  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).
