Poisson-Hopf limit of quantum algebras
Quantum Algebra
2015-05-13 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0903.2178,
title = {Poisson-Hopf limit of quantum algebras},
author = {A. Ballesteros and E. Celeghini and M. A. del Olmo},
journal= {arXiv preprint arXiv:0903.2178},
year = {2015}
}
Comments
13 pages, no figures