Extended jordanian twists for Lie algebras

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebras ${\mathbf{B}}^{\vee }$ of $sl(N)$ the explicit expressions are obtained for the twist element $\mathcal{F}$, universal $\mathcal{R}$-matrix and the corresponding canonical element $\mathcal{T}$. It is shown that the twisted Hopf algebra ${\mathcal{U}}_{\mathcal{F}}({\mathbf{B}}^{\vee })$ is self dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld-Jimbo quantization to the jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.