Some classes of nilpotent associative algebras

TL;DR

This paper classifies specific types of nilpotent associative algebras, including filiform and quasi-filiform algebras, over fields of characteristic zero, providing a detailed structural understanding.

Contribution

It offers a comprehensive classification of filiform and naturally graded nilpotent associative algebras with particular characteristic sequences, expanding the understanding of their structure.

Findings

Classification of filiform associative algebras of degree k

Classification of naturally graded complex filiform and quasi-filiform nilpotent associative algebras

Descriptions based on characteristic sequences C(A)=(n-2,1,1) and C(A)=(n-2,2)

Abstract

In this paper we classify filiform associative algebras of degree $k$ over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by the characteristic sequence $C(\mathcal{A})=(n-2,1,1)$ or $C(\mathcal{A})=(n-2,2)$.