Thus finite order endomorphisms are semisimple over the complex numbers (as the roots of unity are distinct), and nilpotent endomorphisms are not semisimple, as X ^ k has a repeated root.
Thus finite order endomorphisms are semisimple over the complex numbers (as the roots of unity are distinct); this is a part of representation theory of cyclic groups. Nilpotent endomorphisms are not semisimple, as X ^ k has a repeated root.