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,planck(g) depending explicitly on planck and by taking the appropriate planck → 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su_q^{\cal 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.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- July 2009
- DOI:
- 10.1088/1751-8113/42/27/275202
- arXiv:
- arXiv:0903.2178
- Bibcode:
- 2009JPhA...42A5202B
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematical Physics;
- 17B63;
- 17B37;
- 81R50
- E-Print:
- 13 pages, no figures