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.
Classification :
17B20, 22E60, 52D20, 53D05
Mots-clés :
Trivializations of Lie groups, tangent and cotangent groups, Tulczyjew's triplet
Affiliations des auteurs :
Ogul Esen
1
;
Hasan Gümral
1
1
Department of Mathematics, Yeditepe University, 34755 Atasehir -- Istanbul, Turkey
Ogul Esen; Hasan Gümral. Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions. Journal of Lie Theory, Tome 24 (2014) no. 4, pp. 1115-1160. http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a9/
@article{JOLT_2014_24_4_a9,
author = {Ogul Esen and Hasan 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a9/}
}
TY - JOUR
AU - Ogul Esen
AU - Hasan Gümral
TI - Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions
JO - Journal of Lie Theory
PY - 2014
SP - 1115
EP - 1160
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a9/
ID - JOLT_2014_24_4_a9
ER -
%0 Journal Article
%A Ogul Esen
%A Hasan Gümral
%T Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions
%J Journal of Lie Theory
%D 2014
%P 1115-1160
%V 24
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2014_24_4_a9/
%F JOLT_2014_24_4_a9
