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 <ma...@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 > > > _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
