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An octonionic
construction of $E_8$ and the Lie algebra magic square
Robert A. Wilson, Tevian Dray and Corinne A. Manogue |
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Vol. 20 (2023), No. 2-3, 611–634
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Abstract |
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We give a new construction of the Lie algebra of type , in terms of matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal–Tits magic square of Lie algebras, acting on themselves by commutation. |
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Dedicated to the memory of Jacques Tits |
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Keywords
exceptional Lie algebras, Freudenthal–Tits magic square,
octonions
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Mathematical Subject Classification
Primary: 20G41
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Milestones
Received: 11 April 2022
Revised: 26 September 2022
Accepted: 26 October 2022
Published: 13 September 2023
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Authors |
| Robert A. Wilson | |
| School of Mathematical
Sciences Queen Mary University of London London United Kingdom |
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| Tevian Dray | |
| Department of Mathematics Oregon State University Corvallis, OR United States |
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| Corinne A. Manogue | |
| Department of Physics Oregon State University Corvallis, OR United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
