Naturally graded p-filiform associative algebras

TL;DR

This paper classifies naturally graded p-filiform nilpotent associative algebras of dimension n over the complex numbers, based on their characteristic sequence, expanding understanding of their structure.

Contribution

It provides a detailed description and classification of n-dimensional naturally graded p-filiform nilpotent associative algebras with specific characteristic sequences.

Findings

Classification of p-filiform algebras based on characteristic sequence

Explicit descriptions of algebra structures

Extension of known algebraic classifications

Abstract

In the paper, we describe $n$-dimensional naturally graded nilpotent associative algebras with the characteristic sequence $C(\mathcal{A})=(n-p,1,\dots,1)$ as called $p-$filiform algebras over the field of the complex numbers.