The exceptional Lie algebra $\mathfrak{g}_2$ generated by three generators subject to quadruple relations
N. I. Stoilova, J. Van der Jeugt
TL;DR
This paper presents a simplified description of the exceptional Lie algebra g2 as a free Lie algebra generated by three elements with specific quadruple relations, offering a new perspective on its structure.
Contribution
It introduces a novel presentation of g2 using free Lie algebra and quadruple relations, simplifying its understanding and potential computations.
Findings
g2 can be generated by three elements with quadruple relations
The presentation simplifies the algebra's structural understanding
Potential for easier computations and applications in Lie theory
Abstract
In this short communication we show how the Lie algebra can easily be described as a free Lie algebra on 3 generators, subject to some simple quadruple relations for these generators.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry