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Hamiltonian dynamics on matched pairs

Oğul Esen

Department of Mathematics, Gebze Technical University, 41400 Gebze-Kocaeli, Turkey

E-mail Address: oesen@gtu.edu.tr

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and

Serkan Sütlü

Department of Mathematics, Işık University, 34980 Şile-İstanbul, Turkey

E-mail Address: serkan.sutlu@isikun.edu.tr

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https://doi.org/10.1142/S0219887816501280Cited by:15 (Source: Crossref)

Abstract

The cotangent bundle of a matched pair Lie group, and its trivialization, are shown to be a matched pair Lie group. The explicit matched pair decomposition on the trivialized bundle is presented. On the trivialized space, the canonical symplectic two-form and the canonical Poisson bracket are explicitly written. Various symplectic and Poisson reductions are perfomed. The Lie–Poisson bracket is derived. As an example, Lie–Poisson equations on $𝔰 𝔩 {(2, ℂ)}^{*}$ are obtained.

Keywords:

AMSC: 70H05, 70H33, 37J15, 22E70

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