Anticommutative Engel algebras of the first five levels

TL;DR

This paper classifies anticommutative Engel algebras up to the fifth degeneration level, revealing that all such algebras are nilpotent Malcev algebras, thus advancing understanding of their structure.

Contribution

It provides a complete classification of anticommutative Engel algebras at the first five levels, identifying them as nilpotent Malcev algebras, which is a novel structural insight.

Findings

All classified algebras are nilpotent Malcev algebras

Complete classification up to the fifth degeneration level

Enhanced understanding of algebraic structure and hierarchy

Abstract

Anticommutative Engel algebras of the first five degeneration levels are classified. All algebras appearing in this classification are nilpotent Malcev algebras.