Extended Jordanian twists for Lie algebras

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B-boolean OR of sl(N) the explicit expressions are obtained for the twist element F, universal R-matrix and the corresponding canonical element T. It is shown that the twisted Hopf algebra U-F(B-boolean OR) 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.(C) 1999 American Institute of Physics. [S0022-2488(99)02707-3].