The classification of $n$-dimensional nilpotent non-Tortkara anticommutative algebras with $(n-4)$-dimensional annihilator

TL;DR

This paper provides a complete classification of certain nilpotent non-Tortkara anticommutative algebras over the complex numbers, focusing on those with an annihilator of dimension four less than the algebra.

Contribution

It offers the first comprehensive classification of $n$-dimensional nilpotent non-Tortkara anticommutative algebras with a specific annihilator dimension over $ extbf{C}$.

Findings

Complete classification of the specified algebras

Identification of algebra structures with given properties

Framework for understanding nilpotent non-Tortkara anticommutative algebras

Abstract

In this paper, we give a complete classification of $n$-dimensional nilpotent non-Tortkara anticommutative algebras with $(n-4)$-dimensional annihilator over $\mathbb{C}$.