Values of the length function for nonassociative algebras

TL;DR

This paper investigates the possible values of the length function in unital nonassociative algebras, providing conditions for realizability and classifying those with maximal length.

Contribution

It introduces new methods using characteristic sequences and algebraic constructions to determine realizable length values and classifies maximal length unital algebras.

Findings

Established sufficient conditions for length realizability.

Developed a classification of unital algebras with maximal length.

Applied binary decompositions to analyze length functions.

Abstract

We study realizable values of the length function for unital possibly nonassociative algebras of a given dimension. To do this we apply the method of characteristic sequences and establish sufficient conditions of realisability for a given value of length. The proposed conditions are based on binary decompositions of the value and algebraic constructions that allow to modify length function of an algebra. Additionally we provide a classification of unital algebras of maximal possible length in terms of their basis.