Journal of Lie Theory
Vol. 13, No. 1, pp. 155--165 (2003)
A Combinatorial Construction of $G_2$
N. J. WildbergerN. J. Wildberger
School of Mathematics
Sydney 2052 Australia
Abstract: 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.
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Electronic fulltext finalized on: 22 Nov 2002. This page was last modified: 3 Jan 2003.