Automorphisms of real semisimple Lie algebras and their restricted root systems

2022/08/01 by Ivan Solonenko, Solonenko, Ivan
Chemistry · Mathematics · #17B40 (Primary) 17B22 #53C35 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Carbohydrate Chemistry and Synthesis #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2208.01131

openalex publication_date 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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