2022/05/16 by Karl‐Hermann Neeb, Neeb, Karl-Hermann, Gestur Ólafsson +1
Mathematics · #2021 #22E45 #81R05 #81T05 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2205.07685
openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This article is part of an ongoing project aiming at the connections between causal structures on homogeneous spaces, Algebraic Quantum Field Theory (AQFT), modular theory of operator algebras and unitary representations of Lie groups. In this article we concentrate on non-compactly causal symmetric space G/H. This class contains the de Sitter space but also other spaces with invariant partial ordering. The central ingredient is an Euler element h in the Lie algebra of \fg. We define three different kinds of wedge domains depending on h and the causal structure on G/H. Our main result is that the connected component containing the base point eH of those seemingly different domains all agree. Furthermore we discuss the connectedness of those wedge domains. We show that each of those spaces has a natural extension to a non-compactly causal symmetric space of the form G_\C/Gc where Gc is certain real form of the complexification G_$ of G. As G_\C/Gc is non-compactly causal it also comes with the three types of wedge domains. Our results says that the intersection of those domains with G/H agrees with the wedge domains in G/H.