\def\g{{\frak g}} A Lie group $G$ equipped with a left invariant symplectic form $\omega^{+}$ is called a symplectic Lie group and the pair $(\g,\omega)$, where $\g$ is its Lie algebra, the tangent space to $G$ at the unit $\varepsilon$, is said a symplectic Lie algebra. Among others things, we determine connected and simply connected symplectic Lie groups of dimension four which have discrete cocompact subgroups, that is, uniform lattices. We describe in the solvable non nilpotent case, all isomorphy classes of lattices $\Gamma$ and in this fashion obtain an infinity of nonhomeomorphic compact symplectic solvmanifolds. Finally we show that these four dimensional symplectic Lie groups have left invariant symplectic affine structures, that is, left invariant flat and torsion free symplectic connexions.
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Dép. de Mathématiques, Université de Montpellier II, Case Courrier 051, UMR CNRS 5149, 34090 Montpellier, France
Alberto Medina; Phillip Revoy. Lattices in Symplectic Lie Groups. Journal of Lie Theory, Tome 17 (2007) no. 1, pp. 27-39. http://geodesic.mathdoc.fr/item/JOLT_2007_17_1_a1/
@article{JOLT_2007_17_1_a1,
author = {Alberto Medina and Phillip Revoy},
title = {Lattices in {Symplectic} {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {27--39},
year = {2007},
volume = {17},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_1_a1/}
}
TY - JOUR
AU - Alberto Medina
AU - Phillip Revoy
TI - Lattices in Symplectic Lie Groups
JO - Journal of Lie Theory
PY - 2007
SP - 27
EP - 39
VL - 17
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2007_17_1_a1/
ID - JOLT_2007_17_1_a1
ER -
%0 Journal Article
%A Alberto Medina
%A Phillip Revoy
%T Lattices in Symplectic Lie Groups
%J Journal of Lie Theory
%D 2007
%P 27-39
%V 17
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2007_17_1_a1/
%F JOLT_2007_17_1_a1
