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arXiv · 2401.15256

Standard automorphisms of semisimple Lie algebras and their relations

David Reynoso-Mercado
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Abstract

Let $\mathfrak{g}$ be the simple Lie algebra of square matrices $(n+1)\times (n+1)$ with zero trace. There are certain relations concerning standard automorphisms that are considered ``folklore". One can find a complete proof of these in Millson and Toledano Laredo's work [Transformation Groups, Vol. 10, No. 2, 2005, pp. 217-254], but said proof is based on topological arguments which are non-trivial. The aim of this work is to verify these relations in an elementary way.

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David Reynoso-Mercado. 2024-01-27. Standard automorphisms of semisimple Lie algebras and their relations. https://arxiv.org/abs/2401.15256

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