On the solvability of graded Novikov algebras

We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a G-graded Novikov algebra N over a field K with solvable 0-component N0 is solvable, where G is a finite additive abelean group and the characteristic of K does not divide the order of the group G. We also show that any Novikov algebra N with a finite solvable group of automorphisms G is solvable if the algebra of invariants NG is solvable.