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| HAL: hal-00330636, version 1 |
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| Advances in Mathematics 201, 1 (2006) 143-179 |
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| The sextonions and E7 1/2 |
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| Joseph M. Landsberg 1Laurent Manivel 2 |
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| (2006-03-15) |
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| 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 $G_2$. |
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| 1: | Department of Mathematics, Texas A&M University (TAMU) |
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Météo France |
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| 2: | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| Subject | : | Mathematics/Algebraic Geometry |
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| exceptional Lie algebra – octonion – sextonion – Freudenthal's magic square |
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| Attached file list to this document: | ||||||||||
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| hal-00330636, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00330636 | |
| oai:hal.archives-ouvertes.fr:hal-00330636 | |
| From: Laurent Manivel | |
| Submitted on: Wednesday, 15 October 2008 10:35:07 | |
| Updated on: Wednesday, 15 October 2008 11:52:18 | |
