# Quantum algebras as quantizations of dual Poisson–Lie groups

@article{Ballesteros2013QuantumAA,
title={Quantum algebras as quantizations of dual Poisson–Lie groups},
author={{\'A}ngel Ballesteros and Fabio Musso},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2013},
volume={46}
}
• Published 16 December 2012
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
A systematic computational approach for the explicit construction of any quantum Hopf algebra (Uz(g), Δz) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δz is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λg) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by…
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