
Journal of Lie Theory 22 (2012), No. 2, 437463 Copyright Heldermann Verlag 2012 Invariant Orders on Hermitian Lie Groups Gabi Ben Simon Departement Mathematik, ETH Zürich, Rämistr. 101, 8092 Zürich, Switzerland gabi.ben.simon@math.ethz.ch Tobias Hartnick Mathematics Department, Technion, Haifa 3200, Israel tobias.hartnick@gmail.com We study three natural biinvariant 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 SL_{2}(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. Keywords: Hermitian Lie groups, invariant orders, quasimorphisms, Lie semigroups, bounded cohomology. MSC: 06A06, 06F15, 11E57, 22E46, 51L99 [ Fulltextpdf (366 KB)] for subscribers only. 