A(2n+1)-dimensional quantum group constructed from a skew-symmetric matrix
| Autor: | Byung-Jay Kahng |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Mathematics::Operator Algebras Canonical quantization Locally compact quantum group General Physics and Astronomy Algebra Poisson bracket Mathematics::Quantum Algebra Unitary group Geometry and Topology Compact quantum group Poisson–Lie group Mathematical Physics Moyal bracket Mathematics Poisson algebra |
| Zdroj: | Journal of Geometry and Physics. 61:2081-2097 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2011.06.010 |
| Popis: | Beginning with a skew-symmetric matrix, we define a certain Poisson–Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or “Lie–Poisson”) Poisson bracket. By analyzing this Poisson structure, we gather enough information to construct a C ∗ -algebraic locally compact quantum group, via the “cocycle bicrossed product construction” method. The quantum group thus obtained is shown to be a deformation quantization of the Poisson–Lie group, in the sense of Rieffel. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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