Journal of Lie Theory 13 (2003), No. 1, 155--165
Copyright Heldermann Verlag 2003
A Combinatorial Construction of G2
N. J. Wildberger
School of Mathematics, UNSW, Sydney 2052, Australia
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.
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