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

In this paper we consider the representation theory of a non-standard quantization of sl(2)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)sl(2). The results of this paper are used extensively in [4] to study Topological Quantum Field Theory (TQFT) and have connections with Conformal Field Theory (CFT).