Poisson-Hopf limit of quantum algebras

Details Poisson-Hopf limit of quantum algebras Poisson-Hopf limit of quantum algebras

2009-03-12

arxiv.org/abs/0903.2178v1

Mathematics

Quantum Algebra

13 pages, no figures

Scientific paper

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.

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