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Currently displaying 1 – 4 of 4

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A symplectic representation of $E_{7}$

Tevian Dray; Corinne A. Manogue; Robert 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.

Matrix generators for the Harada-Norton group.

Ryba, Alexander J.E.; Wilson, Robert A. — 1994

Experimental Mathematics

Standard generators for $J_{3}$ .

Suleiman, Ibrahim A.I.; Wilson, Robert A. — 1995

Experimental Mathematics

Construction of the fourfold cover of the Mathieu group $M_{22}$ .

Suleiman, Ibrahim A.I.; Wilson, Robert A. — 1993

Experimental Mathematics

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