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Octonions and the reprezentation of Lie algebra g2
Author

Srdjan Vukmirovic
Organization: Faculty of Mathematics, Belgrade
URL: http://alas.matf.bg.ac.yu/~vsrdjan/
Revision date

2004-05-20
Description

This notebook has a dual purpose. As first, it roughly implements the octonionic multiplication and calculates the commutator relations of the Lie algebra g2. As second, it is an advanced example of Mathematica's power in calculations that often happen in Geometry when the problem is reduced to Linear Algebra level (matrices). Besides, a homogenous representation of the sphere S6 using octonions is given.
Subject

*Mathematics > Calculus and Analysis > Differential Geometry
Keywords

octonions, octaves, Cayley numbers, Lie algebra g2, six sphere, derivations
URL

http://math.ucr.edu/home/baez/octonions/octonions.html
http://mathworld.wolfram.com/Octonion.html

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OctonionsAndG2.nb (46.4 KB) - Mathematica Notebook