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.
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