Canonical structure constants for simple Lie algebras

Meinolf Geck; Alexander Lang

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arXiv · 2404.07652

Canonical structure constants for simple Lie algebras

Meinolf Geck·Alexander Lang

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Abstract

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$. In the 1950s Chevalley showed that $\mathfrak{g}$ admits particular bases, now called ``Chevalley bases'', for which the corresponding structure constants are integers. Such bases are not unique but, using Lusztig's theory of canonical bases, one can single out a ``canonical'' Chevalley basis which is unique up to a global sign. In this paper, we give explicit formulae for the structure constants with respect to such a basis.

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Meinolf Geck, Alexander Lang. 2024-04-11. Canonical structure constants for simple Lie algebras. https://arxiv.org/abs/2404.07652

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