Journal of Lie Theory 24 (2014), No. 4, 1115--1160
Copyright Heldermann Verlag 2014
Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions
Ogul Esen
Department of Mathematics, Yeditepe University, 34755 Atasehir -- Istanbul, Turkey
oesen@yeditepe.edu.tr
Hasan Gümral
Department of Mathematics, Yeditepe University, 34755 Atasehir -- Istanbul, Turkey
hgumral@yeditepe.edu.tr
All semidirect product and functorial trivializations of first order and iterated bundles over a Lie group are presented. For cotangent bundles, symplectic reduction is applied to obtain coadjoint orbit symplectic structure. All ingredients of Tulczyjew's triplet namely, iterated bundles, symplectomorphisms and special symplectic structures, for a Lie group are realized in trivializations. Symplectic reductions of iterated bundles by right invariance results in Tulczyjew's triplet for reduced manifolds. Results for left invariance are summarized in an appendix.
Keywords: Trivializations of Lie groups, tangent and cotangent groups, Tulczyjew's triplet.
MSC: 17B20, 22E60, 52D20, 53D05
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