English

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