Naturally graded Zinbiel algebras with nilindex $n-3$

TL;DR

This paper classifies a specific subclass of naturally graded Zinbiel algebras with nilindex n-3, completing the broader classification of such algebras with this nilindex.

Contribution

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

Findings

Classification of a subclass of Zinbiel algebras achieved.

Completes the classification for nilindex n-3.

Defines the characteristic sequence (n-3,2,1).

Abstract

We present the classification of a subclass of $n$-dimensional naturally graded Zinbiel algebras. This subclass has the nilindex $n-3$ and the characteristic sequence $(n-3,2,1).$ In fact, this result completes the classification of naturally graded Zinbiel algebras of nilindex $n-3.$