# 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.

## Key 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.