1School of Mathematics, UNSW, Sydney 2052, Australia 2We show how to construct the simple exceptional Lie algebra of type G 3by 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. 4[
Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 155-165
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N. J. Wildberger. A Combinatorial Construction of G2. Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 155-165. http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a8/
@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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a8/}
}
TY - JOUR
AU - N. J. Wildberger
TI - A Combinatorial Construction of G2
JO - Journal of Lie Theory
PY - 2003
SP - 155
EP - 165
VL - 13
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a8/
ID - JOLT_2003_13_1_a8
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%J Journal of Lie Theory
%D 2003
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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.
