Automorphisms of real semisimple Lie algebras and their restricted root systems
Differential Geometry
2022-08-22 v2
Abstract
We prove that every automorphism of the restricted root system of a real semisimple Lie algebra -- when defined properly -- can be lifted to an automorphism of that Lie algebra. In particular, this can be applied to automorphisms of the Dynkin diagram of the restricted root system. We also discuss some applications of this result to the theory of symmetric spaces of noncompact type.
Keywords
Cite
@article{arxiv.2208.01131,
title = {Automorphisms of real semisimple Lie algebras and their restricted root systems},
author = {Ivan Solonenko},
journal= {arXiv preprint arXiv:2208.01131},
year = {2022}
}
Comments
28 pages. Minor changes. A few misprints corrected