Comodules of Uq(sl2) and modules of SLq(2) via quiver methods

The aim of this paper is to construct comodules of U-q (Sl(2)) and modules of SLq (2) via quiver, where q is not a root of unity. By embedding Uq (Sl(2)) into the path coalgebra kD(C), where D is the Gabriel quiver of Uq (Sl(2)) as a coalgebra, we obtain a basis of Uq (sl(2)) in terms of combinations of paths of the quiver D; this special basis enables us to describe the category of Uq (Sl(2))comodules by certain representations of D; and this description further permits us to construct a class of modules of SLq (2), from certain representations of D, via the duality between Uq (sl(2)) and SLq (2). (c) 2007 Elsevier B.V. All rights reserved.