A simple way to compute structure constants of semi-simple Lie algebras

2020/11/16 by Bill Casselman, Casselman, Bill
Mathematics · #17B05 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2011.08274

openalex publication_date 2020/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The standard way to compute the structure constants of semi-simple Lie algebras involves the additive structure of the roots. In earlier work, I described how ideas of Jacques Tits could be applied to do this by using the structure of the Weyl group. In this work, I explain how to combine some of the earlier ideas with some suggestions of Kottwitz to present a very simple algorithm which comes close to constructing a canonical basis of the Lie algebra. Unfortunately, unlike previous methods, it does not work for arbitrary Kac-Moody algebra.

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