On the Lie-solvability of Novikov algebras

Abstract

We prove that any Novikov algebra over a field of characteristic $\ne 2$ 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 $[N,N]$.

11 pages. arXiv admin note: text overlap with arXiv:2103.07464