2015/12/21 by Oğul Esen, Esen, Oğul, Serkan Sütlü +1
Mathematics · Physics and Astronomy · #37J15 #70H03 #76M60 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:37J15 #msc:70H03 #msc:76M60
paper · pdf · doi:10.48550/arxiv.1512.06770
arxiv created 2016/10/03 · arxiv updated 2016/10/04
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).