Reductive radical of evolution algebras

Abstract

t. We consider M(A), the intersection of all maximal ideals of an evolution algebra A and study the structure of the quotient A/ M(A), which turns out to be a reductive algebra. By using subdirect products we state structure theorems for arbitrary evolution algebras (arbitrary dimension and ground field), one of them in terms of Grassmannians. Specializing in the perfect finite-dimensional case, we obtain a direct sum decomposition instead of a subdirect product and, furthermore, the uniqueness of this decomposition. We also study some examples that exhibit a richer structure with a nonzero semisimple part.