### Abstract

A Poisson realization of the simple real Lie algebra so^{*}(4n) on the phase space of each Sp(1)-Kepler problem is exhibited. As a consequence, one obtains the Laplace-Runge- Lenz vector for each classical Sp(1)-Kepler problem. The verification of these Poisson realizations is greatly simplified via an idea ofWeinstein. The totality of these Poisson realizations is shown to be equivalent to the canonical Poisson realization of so^{*}(4n) on the Poisson manifold T^{*}H_{*} ^{n}/Sp(1). (Here H_{*} ^{n}:= H^{n}\(0) and the Hamiltonian action of Sp(1) on T^{*}H_{*} ^{n} is induced from the natural right action of Sp(1) on H_{*} ^{n}.) Published by AIP Publishing.

Original language | English (US) |
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Article number | 1.5001688 |

Journal | Journal of Mathematical Physics |

Volume | 58 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2017 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*58*(9), [1.5001688]. https://doi.org/10.1063/1.5001688

**The classical dynamic symmetry for the Sp(1)-kepler problems.** / Bouarroudj, Sofiane; Meng, Guowu.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 58, no. 9, 1.5001688. https://doi.org/10.1063/1.5001688

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TY - JOUR

T1 - The classical dynamic symmetry for the Sp(1)-kepler problems

AU - Bouarroudj, Sofiane

AU - Meng, Guowu

PY - 2017/9/1

Y1 - 2017/9/1

N2 - A Poisson realization of the simple real Lie algebra so*(4n) on the phase space of each Sp(1)-Kepler problem is exhibited. As a consequence, one obtains the Laplace-Runge- Lenz vector for each classical Sp(1)-Kepler problem. The verification of these Poisson realizations is greatly simplified via an idea ofWeinstein. The totality of these Poisson realizations is shown to be equivalent to the canonical Poisson realization of so*(4n) on the Poisson manifold T*H* n/Sp(1). (Here H* n:= Hn\(0) and the Hamiltonian action of Sp(1) on T*H* n is induced from the natural right action of Sp(1) on H* n.) Published by AIP Publishing.

AB - A Poisson realization of the simple real Lie algebra so*(4n) on the phase space of each Sp(1)-Kepler problem is exhibited. As a consequence, one obtains the Laplace-Runge- Lenz vector for each classical Sp(1)-Kepler problem. The verification of these Poisson realizations is greatly simplified via an idea ofWeinstein. The totality of these Poisson realizations is shown to be equivalent to the canonical Poisson realization of so*(4n) on the Poisson manifold T*H* n/Sp(1). (Here H* n:= Hn\(0) and the Hamiltonian action of Sp(1) on T*H* n is induced from the natural right action of Sp(1) on H* n.) Published by AIP Publishing.

UR - http://www.scopus.com/inward/record.url?scp=85029476152&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029476152&partnerID=8YFLogxK

U2 - 10.1063/1.5001688

DO - 10.1063/1.5001688

M3 - Article

VL - 58

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 1.5001688

ER -