Poisson-Hopf limit of quantum algebras

Abstract

The Poisson-Hopf analogue of an arbitrary quantum algebra U_z(g) is constructed by introducing a one-parameter family of quantizations U_{z,h}(g) depending explicitly on h and by taking the appropriate h -> 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su_q^P (3) case is introduced. The q-Serre relations are also extended to the Poisson limit. This approach opens the perspective for possible applications of higher rank q-deformed Hopf algebras in semiclassical contexts.

13 pages, no figures

References in corpus (6)

• The Drinfeld double gl(n) \oplus t_n
• Classical Lie algebras and Drinfeld doubles
• SU(3) Richardson-Gaudin models: three level systems
• From Quantum Universal Enveloping Algebras to Quantum Algebras
• The Gell-Mann-Okubo and Colemann-Glashow relations for octet and decuplet baryons in the $S{U}_q(3)$ quantum algebra
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Cited by in corpus (3)

• On classical q-deformations of integrable sigma-models
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Quantum $S{L}_2$, Infinite curvature and Pitman's 2M-X theorem