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Advances in Mathematics 201, 1 (2006) 143-179

The sextonions and E7 1/2

Joseph M. Landsberg 1, Laurent Manivel 2

(15/03/2006)

We fill in the hole in the exceptional series of Lie algebras that was observed by Cvitanovic, Deligne, Cohen and deMan. More precisely, we show that the intermediate Lie algebra between $E_7$ and $E_8$ satisfies some of the decomposition and dimension formulas of the exceptional simple Lie algebras. A key role is played by the sextonions, a six dimensional algebra between the quaternions and octonions. Using the sextonions, we show simliar results hold for the rows of an expanded Freudenthal magic chart. We also obtainnew interpretations of the adjoint variety of the exceptional group $G_2$.

1 :	Department of Mathematics, Texas A&M University (TAMU)
	Météo France
2 :	Institut Fourier (IF)
	CNRS : UMR5582 – Université Joseph Fourier - Grenoble I

Domaine

:

Mathématiques/Géométrie algébrique

Mots Clés : exceptional Lie algebra – octonion – sextonion – Freudenthal's magic square

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Contributeur : Laurent Manivel <>

Soumis le : Mercredi 15 Octobre 2008, 10:35:07

Dernière modification le : Mercredi 15 Octobre 2008, 11:52:18