Solvability and nilpotency of Novikov algebras

Abstract

We first prove that a left Novikov algebra is right nilpotent if and only if it is solvable. Then we show that, every Novikov algebra that can be represented as the sum of two solvable subalgebras is itself solvable, moreover, if the two solvable subalgebras are abelian, then the whole algebra is metabelian. Finally, we show that for every every n-generated non-abelian free solvable (or non-abelian free right nilpotent) Novikov algebra has wild automorphisms.