Classical and quantum duality in jordanian quantizations

Abstract

The limiting transitions between different types of quantizations are studied by the deformation theory methods. We prove that for the first order coboundary deformation (g,g*_1 + x g*_2) of a Lie bialgebra (g,g*) one can always get the quantized Lie bialgebra (g,g*_2) as a limit of the sequence of quantizations of the type A(g,g*_1). The obtained results are illustrated by some low-dimensional examples of quantized Lie algebras and superalgebras.

9 pages, Latex, presented at the VII-th Colloquium "Quantum Groups and Integrable Systems",Prague 18 - 20 June 1998, to be published in Czech. Journal of Physics

References in corpus (2)

• Extended jordanian twists for Lie algebras
• Super-jordanian deformation of the orthosymplectic Lie superalgebras

Cited by in corpus (5)

• Chains of twists for classical Lie algebras
• Peripheric Extended Twists
• Extended and Reshetikhin Twists for sl(3)
• Quantum Jordanian twist
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish