On the Lie-solvability of Novikov algebras

TL;DR

This paper characterizes when Novikov algebras are Lie-solvable, linking it to the nilpotency of their commutator ideal, and provides examples of infinite-dimensional cases with non-nilpotent commutator ideals.

Contribution

It establishes a precise criterion for Lie-solvability of Novikov algebras based on the nilpotency of their commutator ideal and constructs relevant examples.

Findings

Novikov algebras over fields with characteristic not 2 are Lie-solvable iff their commutator ideal is right nilpotent.

Constructs of infinite-dimensional Lie-solvable Novikov algebras with non-nilpotent commutator ideals.

Provides a complete characterization of Lie-solvability in Novikov algebras.

Abstract

We prove that any Novikov algebra over a field of characteristic $\neq 2$ is Lie-solvable if and only if its commutator ideal $[N,N]$ is right nilpotent. We also construct examples of infinite-dimensional Lie-solvable Novikov algebras $N$ with non nilpotent commutator ideal $[N,N]$.