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arXiv · 2312.15226

The Table of the Structure Constants for the Complex Simple Lie Algebra of Type G_2 and Chevalley Commutator Formulas in the Chevalley Group of Type G_2 over a Field

Sergey G. Kolesnikov
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Abstract

This article is the second in the series and is devoted to the type G_2. The work consists of two parts. In the first part we calculate the structure constants of the complex simple Lie algebra of type G_2. All structure constants are represented as functions of the structure constants corresponding to extraspecial pairs. The results obtained are used to calculate the commutator Chevalley formulas for [x_r(u),x_s(y)], when the sum r+s is a root. Further, in the second part there is a table of structure constants and Chevalley commutator formulas in the special case, when all structure constants corresponding to extraspecial pairs are positive.

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Sergey G. Kolesnikov. 2023-12-23. The Table of the Structure Constants for the Complex Simple Lie Algebra of Type G_2 and Chevalley Commutator Formulas in the Chevalley Group of Type G_2 over a Field. https://arxiv.org/abs/2312.15226

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