The type and several invariant subspaces related to the upper annihilating
series of finite-dimensional nilpotent evolution algebras are introduced. These
invariants can be easily computed from any natural basis. Some families of
nilpotent evolution algebras, defined in terms of a nondegenerate symmetric
bilinear form and some commuting symmetric diagonalizable endomorphisms
relative to the form, are explicitly constructed. Both the invariants and these
families are used to review and complete the classification of nilpotent
evolution algebras up to dimension five over algebraically closed fields.Comment: 19 page
