Journal of Lie Theory

no. 4
Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions
Journal of Lie Theory, Volume 24 (2014) no. 4, pp. 1115-1160
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.
DOI: 10.5802/jolt.821
Classification: 17B20, 22E60, 52D20, 53D05
Keywords: Trivializations of Lie groups, tangent and cotangent groups, Tulczyjew's triplet 
@article{JOLT_2014_24_4_a9,
     author = {O. Esen and H. G\"umral},
     title = {Tulczyjew's {Triplet} for {Lie} {Groups} {I:} {Trivializations} and {Reductions}},
     journal = {Journal of Lie Theory},
     pages = {1115--1160},
     year = {2014},
     volume = {24},
     number = {4},
     doi = {10.5802/jolt.821},
     zbl = {1357.53091},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.821/}
}
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O. Esen; H. Gümral. Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions. Journal of Lie Theory, Volume 24 (2014) no. 4, pp. 1115-1160. doi: 10.5802/jolt.821

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