Evolution algebras, automorphisms, and graphs

Abstract

The affine group scheme of automorphisms of an evolution algebra with is shown to lie in an exact sequence , where , diagonalizable, and , constant, depend solely on the directed graph associated to . As a consequence, the Lie algebra of derivations (with ) 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.