Crowned Lie groups and nets of real subspaces

Beltiţă D, Neeb KH (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Annals of Global Analysis and Geometry Springer Verlag (Germany)

Book Volume: 70

Article Number: 5

Journal Issue: 2

DOI: 10.1007/s10455-026-10052-5

Abstract

We introduce the notion of a complex crown domain for a connected Lie group G, and we use analytic extensions of orbit maps of antiunitary representations to these domains to construct nets of real subspaces on G that are isotone, covariant and satisfy the Reeh–Schlieder and Bisognano–Wichmann conditions from Algebraic Quantum Field Theory. This provides a unifying perspective on various constructions of such nets. The representation theoretic properties of different crowns are discussed in some detail for the non-abelian 2-dimensional Lie group Aff(R). We also characterize the existence of nets with the above properties by a regularity condition in terms of an Euler element in the Lie algebra g and show that all antiunitary representations of the split oscillator group have this property.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

"Gheorghe Mihoc - Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy

Romania (RO)

How to cite

APA:

Beltiţă, D., & Neeb, K.H. (2026). Crowned Lie groups and nets of real subspaces. Annals of Global Analysis and Geometry, 70(2). https://doi.org/10.1007/s10455-026-10052-5

MLA:

Beltiţă, Daniel, and Karl Hermann Neeb. "Crowned Lie groups and nets of real subspaces." Annals of Global Analysis and Geometry 70.2 (2026).

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