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A structure theorem for right pp-semigroups with left central idempotents

Xue Ming Ren, Kar-Ping Shum (2000)

Discussiones Mathematicae - General Algebra and Applications

The concept of strong spined product of semigroups is introduced. We first show that a semigroup S is a rpp-semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes. Then, we show that such kind of semigroups can be described by the strong spined product of a C-rpp-semigroup and a right normal band. In particular, we show that a semigroup is a rpp-semigroup with left central idempotents if and only if it is a right bin.

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.

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