Classification of naturally graded nilpotent associative algebras

Abstract

In the paper, we consider $n-$ dimensional naturally graded nilpotent associative algebras with the characteristic sequence $C(\mathcal{A})=(n-m,m)$ over an algebraically closed field of characteristic zero. There are two types of such algebras. We give the algebraic classification up to isomorphism of both types of algebras. Moreover, we prove that there are no such algebras of the second type for $n>2m+1$.

KEYWORD:

• Associative algebras
• characteristic sequence
• filiform
• left multiplication operator
• naturally graded
• nilpotent
• null-filiform
• quasi-filiform

2020MATHEMATICS SUBJECT CLASSIFICATION:

• 16S50
• 16W50