Invariant Orders on Hermitian Lie Groups

Abstract

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 $S{L}_2(\mathbb{R})$ we can show that they coincide.

Revised version, to appear in Journal of Lie Theory

References in corpus (1)

• Quasi-Total Orders and Translation Numbers

Cited by in corpus (2)

• Quasi-state Rigidity for Finite-dimensional Lie Algebras
• A Family of Quasimorphism Constructions