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

Bill Casselman

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arXiv · 2011.08274

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

Bill Casselman

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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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Bill Casselman. 2020-11-16. A simple way to compute structure constants of semi-simple Lie algebras. https://arxiv.org/abs/2011.08274

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