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

Francesco Costantino (1) , Nathan Geer , Bertrand Patureau-Mirand (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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).

Domaines: Algèbres quantiques [math.QA]

Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand. Some remarks on the unrolled quantum group of sl(2). Journal of Pure and Applied Algebra, 2014, pp.Available online. ⟨10.1016/j.jpaa.2014.10.012⟩. ⟨hal-00998928⟩