Journal of Lie Theory

no. 1
A Combinatorial Construction of G2
Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 155-165
We show how to construct the simple exceptional Lie algebra of type  G2  by explicitly constructing its 7 dimensional representation. Technically no knowledge of Lie theory is required. The structure constants have a combinatorial meaning involving convex subsets of a partially ordered multiset of six elements. These arise from playing the Numbers and Mutation games on a certain directed multigraph.
DOI: 10.5802/jolt.295
Classification: 17B25
Keywords: simple exceptional Lie algebra of type \(G_2\), 7 dimensional representation, directed multigraph 
@article{JOLT_2003_13_1_a8,
     author = {N. J. Wildberger},
     title = {A {Combinatorial} {Construction} of {G\protect\textsubscript{2}}},
     journal = {Journal of Lie Theory},
     pages = {155--165},
     year = {2003},
     volume = {13},
     number = {1},
     doi = {10.5802/jolt.295},
     zbl = {1032.17015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.295/}
}
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N. J. Wildberger. A Combinatorial Construction of G2. Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 155-165. doi: 10.5802/jolt.295

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