The Freiheitssatz for Novikov algebras

TL;DR

This paper proves the Freiheitssatz for Novikov algebras over characteristic zero fields and shows that their variety is generated by a specific polynomial algebra-based Novikov algebra, establishing a base rank of 1.

Contribution

It establishes the Freiheitssatz for Novikov algebras and identifies a generating algebra with base rank 1, advancing the structural understanding of these algebras.

Findings

Freiheitssatz holds for Novikov algebras in characteristic zero.

The variety of Novikov algebras is generated by a polynomial algebra-based Novikov algebra.

The base rank of the variety is exactly 1.

Abstract

We prove the Freiheitssatz for Novikov algebras in characteristic zero. It is also proved that the variety of Novikov algebras is generated by a Novikov algebra on the space of polynomials $k[x]$ in a single variable $x$ over a field $k$ with respect to the multiplication $f\circ g=\partial(f)g$. It follows that the base rank of the variety of Novikov algebras equals 1.