The adjoint representation of quantum algebra Uq(sl(2))

Abstract

Starting from any representation of the Lie algebra g on the finite dimensional vector space V we can construct the representation on the space Aut(V). These representations are of the type of ad. That is one of the reasons, why it is important to study the adjoint representation of the Lie algebra g on the universal enveloping algebra U(g). A similar situation is for the quantum groups Uq(g). In this paper, we study the adjoint representation for the simplest quantum algebra Uq(sl(2)) in the case that q is not a root of unity. © Č. Burdík, O. Navrátil and S. Pošta.