[GAP Forum] G2(3) from OctaveAlgebra(GF(3))

[Marek Mitros]

I should maybe clarify that L(u) is matrix of left multiplication by
element u and R(v) is right multiplication by element v. Element
(L(u)R(v))^2 is involution fixing quaternion subalgebra generated by u and
v.

Regards,
Marek


2018-08-03 11:14 GMT+02:00 Marek Mitros <marek at mitros.org>:

> Hello Wiliam and forum,
>
> There are 702 imaginary unitary elements in octave algebra over GF(3). By
> imaginary unitary element I mean such x that conjugated(x) = -x and norm
> (x) = 1. For each u imaginary unitary there are 252 perpendicular imaginary
> unitary. By "perpendicular" I mean such element v that u*v is also
> imaginary. For such pair u,v matrix (L(u)R(v))^2 is automorphism of
> octonions.
>
> If you take 8 such random matrices then they will generate G2(3) of
> size 4245696.
>
> Regards,
> Marek
>
>
>