CZECHOSLOVAK JOURNAL OF PHYSICS, vol.55, no.4, pp.463-471, 2005 (Journal Indexed in SCI)
We present a differential calculus on the extension of the quantum plane obtained by considering that the (bosonic) generator x is invertible and by working with polynomials in In x instead of polynomials in x. We construct the quantum Lie algebra associated with this extension and obtain its Hopf algebra structure and its dual Hopf algebra.