
Journal of Lie Theory 13 (2003), No. 1, 155165 Copyright Heldermann Verlag 2003 A Combinatorial Construction of G_{2} N. J. Wildberger School of Mathematics, UNSW, Sydney 2052, Australia We show how to construct the simple exceptional Lie algebra of type G_{2} 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. [ Fulltextpdf (177 KB)] for subscribers only. 