We study three natural bi-invariant partial orders on a certain covering group of the automorphism group of a bounded symmetric domain of tube type; these orderings are defined using the geometry of the Shilov boundary, Lie semigroup theory and quasimorphisms respectively. Our main result shows that these orders are related by two inclusion relations. In the case of SL2(R), where R stands for the real numbers, we can show that they coincide. We also prove a related coincidence of orders for the universal covering of the group of homeomorphisms of the circle.
1
Departement Mathematik, ETH Zürich, Rämistr. 101, 8092 Zürich, Switzerland
2
Mathematics Department, Technion, Haifa 3200, Israel
Gabi Ben Simon; Tobias Hartnick. Invariant Orders on Hermitian Lie Groups. Journal of Lie Theory, Tome 22 (2012) no. 2, pp. 437-463. http://geodesic.mathdoc.fr/item/JOLT_2012_22_2_a3/
@article{JOLT_2012_22_2_a3,
author = {Gabi Ben Simon and Tobias Hartnick},
title = {Invariant {Orders} on {Hermitian} {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {437--463},
year = {2012},
volume = {22},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_2_a3/}
}
TY - JOUR
AU - Gabi Ben Simon
AU - Tobias Hartnick
TI - Invariant Orders on Hermitian Lie Groups
JO - Journal of Lie Theory
PY - 2012
SP - 437
EP - 463
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2012_22_2_a3/
ID - JOLT_2012_22_2_a3
ER -
%0 Journal Article
%A Gabi Ben Simon
%A Tobias Hartnick
%T Invariant Orders on Hermitian Lie Groups
%J Journal of Lie Theory
%D 2012
%P 437-463
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2012_22_2_a3/
%F JOLT_2012_22_2_a3
