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arXiv · 1512.06770

Lagrangian Dynamics on Matched Pairs

Oğul Esen·Serkan Sütlü
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Abstract

Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler-Poincaré equations on the matched pair of Lie algebras. We show explicitly how these equations cover those of the semi-direct product theory. In particular, we study the trivialized, and the reduced Lagrangian dynamics on the group $SL(2,\mathbb{C})$.

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Oğul Esen, Serkan Sütlü. 2016-10-03. Lagrangian Dynamics on Matched Pairs. https://arxiv.org/abs/1512.06770

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