Codimension growth of a variety of Novikov algebras

TL;DR

This paper investigates Novikov algebras, constructs their free bases using Young diagrams, and establishes that the codimension growth rate for these algebras has an exponent of 4.

Contribution

It introduces a construction of free Novikov algebras via Young diagrams and proves the existence and value of the codimension growth exponent.

Findings

Codimension exponent for Novikov algebras exists and equals 4.

Constructed free Novikov algebra basis using Young diagrams.

Established growth rate characteristics of Novikov algebra varieties.

Abstract

An algebra with identities $a\circ(b\circ c-c\circ b)=(a\circ b)\circ c-(a\circ c)\circ b$ and $a\circ(b\circ c)=b\circ(a\circ c)$ is called Novikov. We construct free Novikov base in terms of Young diagrams. We show that codimensions exponent for a variety of Novikov algebras exists and is equal 4.