EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 1, pp. 155--165 (2003)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



A Combinatorial Construction of $G_2$

N. J. Wildberger

N. 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.

Full text of the article:

Electronic fulltext finalized on: 22 Nov 2002. This page was last modified: 3 Jan 2003.

© 2002 Heldermann Verlag
© 2002--2003 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition