On the solvability of graded Novikov algebras

TL;DR

This paper investigates conditions under which graded Novikov algebras are solvable, establishing new results on nilpotency and solvability related to subalgebras, gradings, and automorphism groups.

Contribution

It proves that certain subalgebras generate nilpotent ideals and establishes solvability criteria for graded Novikov algebras based on their components and automorphisms.

Findings

Right ideal generated by square of a right nilpotent subalgebra is nilpotent.

A G-graded Novikov algebra with solvable zero component is solvable.

Novikov algebra with a finite solvable automorphism group is solvable if invariants are solvable.

Abstract

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 $N_0$ 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 $N^G$ is solvable.