Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality

Morinelli V, Neeb KH, Ólafsson G (2025)

Publication Type: Journal article

Publication year: 2025

Journal

DOI: 10.1515/forum-2025-0365

Abstract

The current article continues our project on representation theory, Euler elements, causal homogeneous spaces and Algebraic Quantum Field Theory (AQFT). We call a pair (h,k) of Euler elements orthogonal if e^π⁢i⁢adh⁢k=-k. We show that, if (h,k) and (k,h) are orthogonal, then they generate a 3-dimensional simple subalgebra. We also classify orthogonal Euler pairs in simple Lie algebras and determine the fundamental groups of orbits of Euler elements in arbitrary finite-dimensional Lie algebras. Causal complements of wedge regions in spacetimes can be related to so-called twisted complements in the space of abstract Euler wedges, defined in purely group theoretic terms. We show that any pair of twisted complements can be connected by a chain of successive complements coming from 3-dimensional subalgebras.

Authors with CRIS profile

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

Involved external institutions

Università degli Studi di Roma 'Tor Vergata'

Italy (IT) Louisiana State University

United States (USA) (US)

How to cite

APA:

Morinelli, V., Neeb, K.H., & Ólafsson, G. (2025). Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality. Forum Mathematicum. https://doi.org/10.1515/forum-2025-0365

MLA:

Morinelli, Vincenzo, Karl Hermann Neeb, and Gestur Ólafsson. "Orthogonal pairs of Euler elements I. Classification, fundamental groups and twisted duality." Forum Mathematicum (2025).

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