A construction of Exceptional Weyl Group $W\left(F_4\right)$ and $W\left(E_8\right)$ using Quaternion, and the lattice in 16-dimensional Euclidean space

Misaki Ohta

It is mentioned that there is a subalgebra isomorphic to the alternating group $2\cdot A_4$ as a subalgebra of the Quaternion over integers and half-integers called Hurwitz quater…