Extended Jordanian twists for Lie algebras
Abstract
Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebras ${\bf B}^{\vee}$ of $sl(N)$ the explicit expressions are obtained for the twist element ${\cal F}$, universal ${\cal R}$-matrix and the corresponding canonical element ${\cal T}$. It is shown that the twisted Hopf algebra ${\cal U}_{\cal F} ({\bf B}^{\vee})$ 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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- September 1999
- DOI:
- 10.1063/1.532987
- arXiv:
- arXiv:math/9806014
- Bibcode:
- 1999JMP....40.4569K
- Keywords:
-
- 03.65.Fd;
- 02.10.Sp;
- Algebraic methods;
- Mathematics - Quantum Algebra
- E-Print:
- 28 pages, LaTeX