Evolution algebras, automorphisms, and graphs

Abstract

The affine group scheme of automorphisms of an evolution algebra ε with ε 2 is shown to lie in an exact sequence → D → Aut(E) → S, where D, diagonalizable, and S, constant, depend solely on the directed graph associated to ε. As a consequence, the Lie algebra of derivations Der(ε) (with ε 2 = E)is shown to be trivial if the characteristic of the ground field is 0 or 2, and to be abelian, with a precise description, otherwise.