Classical and quantum duality in jordanian quantizations

Details Classical and quantum duality in jordanian quantizations Classical and quantum duality in jordanian quantizations

1998-07-22

arxiv.org/abs/math/9807122v1

Mathematics

Quantum Algebra

9 pages, Latex, presented at the VII-th Colloquium "Quantum Groups and Integrable Systems",Prague 18 - 20 June 1998, to be pub

Scientific paper

10.1023/A:1021613407866

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.

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