Poisson-Hopf limit of quantum algebras

Understand

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.