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A symplectic representation of E 7

Tevian DrayCorinne A. ManogueRobert A. Wilson — 2014

Commentationes Mathematicae Universitatis Carolinae

We explicitly construct a particular real form of the Lie algebra 𝔢 7 in terms of symplectic matrices over the octonions, thus justifying the identifications 𝔢 7 𝔰𝔭 ( 6 , 𝕆 ) and, at the group level, E 7 Sp ( 6 , 𝕆 ) . Along the way, we provide a geometric description of the minimal representation of 𝔢 7 in terms of rank 3 objects called cubies.

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