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Extended jordanian twists for Lie algebras

P. P. Kulish·V. D. Lyakhovsky·A. I. Mudrov
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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.

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BibTeXRIS

P. P. Kulish, V. D. Lyakhovsky, A. I. Mudrov. 1998-06-03. Extended jordanian twists for Lie algebras. https://doi.org/10.1063/1.532987

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