I ask as an undergraduate student the following questions, can I get some simple and satisfying answers ?
what exactly is E8?
how can I learn more about it ?
in my little knowledge about lie groups I read that The Lie group SO(3) is diffeomorphic to the real projective space, is E8 a somewhat similar to that with the rotation matrix
$T=\begin{pmatrix} 0 &0 &0 &1 & & & & \\ 1 &0 &0 &0 & & & & \\ 0 &0 &1 &0 & & & & \\ 0 &1 &0 &0 & & & & \\ & & & & -\frac{1}{\sqrt{2}} &-\frac{\sqrt{3}}{2} & & \\ & & & & \frac{\sqrt{3}}{2} & -\frac{1}{2} & & \\ & & & & & &1 &0 \\ & & & & & & 0 &1 \end{pmatrix}$
“E8 is perhaps the most beautiful structure in all of mathematics, but it’s very complex.” — Hermann Nicolai