Geodesic
Flat Affine Symplectic Lie Groups
Fabricio Valencia1
1Instituto de Matemáticas, Universidad de Antioquia, Medellín 050010, Colombia
Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 63-92

Voir la notice de l'article provenant de la source Heldermann Verlag

We give a new characterization of flat affine manifolds in terms of an action of the Lie algebra of classical infinitesimal affine transformations on the bundle of linear frames. We characterize flat affine symplectic Lie groups using symplectic étale affine representations and as a consequence of this, we show that a flat affine symplectic Lie group with bi-invariant symplectic connection contains a nontrivial one parameter subgroup formed by central translations. We give two methods for constructing flat affine symplectic Lie groups, thus obtaining all those having bi-invariant symplectic connections. We get nontrivial examples of simply connected flat affine symplectic Lie groups in every even dimension.
Classification : 53D05, 53A15, 22E60, 22F30
Mots-clés : Flat affine symplectic structure, flat affine symplectic Lie group, bi-invariant symplectic connection, geodesic completeness

Fabricio Valencia  1

1 Instituto de Matemáticas, Universidad de Antioquia, Medellín 050010, Colombia 
Fabricio Valencia. Flat Affine Symplectic Lie Groups. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 63-92. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a3/
@article{JOLT_2021_31_1_a3,
     author = {Fabricio Valencia},
     title = {Flat {Affine} {Symplectic} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {63--92},
     year = {2021},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a3/}
}
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