Invariant Orders on Hermitian Lie Groups

2010/11/15 by Gabi Ben Simon, Simon, Gabi Ben, Tobias Hartnick +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1011.3505

Revised version, to appear in Journal of Lie Theory

openalex publication_date 2010/11/15 · arxiv created 2011/08/30 · arxiv updated 2011/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 SL₂(\R) we can show that they coincide.

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