Poisson-Hopf limit of quantum algebras
Abstract
The Poisson-Hopf analogue of an arbitrary quantum algebra Uz(g) is constructed by introducing a one-parameter family of quantizations Uz,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 suqP (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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