Quantum anchor : $\uqs$ case

Abstract

We introduce the tangent space $T({\mathrm{H}}_q)$ on the quantum hyperboloid (${\mathcal{A}}_{0,q}^c$) and equip it with an action on ${\mathcal{A}}_{0,q}^c$ being a deformation of the action of vectors fields on functions. An embedding $sl(2{)}_q⟶T({\mathrm{H}}_q)$ of $q$-deformed Lie algebra $sl(2)$ being an analogue of the anchor $ \displaystyle sl(2) \longrightarrow \Vect({\rm H}) $ is called "quantum anchor".

7 pages Latex. To appear in Proceedings of whorkshop on Hopf algebras (1998) at VUB (Belgium)