Naturally graded nilpotent associative algebras of nilindex $n-3$

TL;DR

This paper classifies a specific subclass of naturally graded nilpotent associative algebras with nilindex n-3, completing the broader classification for dimensions greater than six.

Contribution

It provides a complete classification of naturally graded associative algebras with nilindex n-3 and characteristic sequence (n-3,2,1) for n>6.

Findings

Classification of the subclass with characteristic sequence (n-3,2,1)

Completes the classification for nilindex n-3 when n>6

Advances understanding of the structure of nilpotent associative algebras

Abstract

In the present paper, we give the classification of a subclass of n-dimensional naturally graded associative algebras with nilindex $n-3$. The subclass has the characteristic sequence $C(\mathcal{A})=(n-3,2,1)$. The result completes the classification of naturally graded associative algebras with nilindex $n-3$ for $n>6$.