The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator

TL;DR

This paper classifies all $n$-dimensional anticommutative complex algebras with a large annihilator by describing their structure as central extensions of 3-dimensional cases.

Contribution

It provides a complete classification of such algebras, focusing on their structure as central extensions of 3-dimensional anticommutative algebras.

Findings

All $n$-dimensional anticommutative complex algebras with $(n-3)$-dimensional annihilator are classified.

Explicit descriptions of these algebras as central extensions are provided.

The classification extends understanding of the structure of anticommutative algebras.

Abstract

We give the classification of all $n$-dimensional anticommutative complex algebras with $(n-3)$-dimensional annihilator. Namely, we describe all central extensions of all $3$-dimensional anticommutative complex algebras.