Lagrangian dynamics on matched pairs

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• 作者：Oğul Esen^a ; ^{oesen@gtu.edu.tr} ; Serkan S&uuml ; tl&uuml ; ^b ; ^{serkan.sutlu@isikun.edu.tr}
• 关键词：Matched pair of Lie groups ; Matched pair of Lie algebras ; Trivialized Euler&ndash ; Lagrange equations ; Euler&ndash ; Poincaré ; equations ; Lagrangian reduction
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：Complete
• 页码：142-157
• 全文大小：579 K
• 卷排序：111

文摘

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,C)SL(2,C).