The classification of algebras of level two

TL;DR

This paper classifies complex finite-dimensional algebras of level two across Jordan, Lie, and associative varieties, providing a comprehensive understanding of their structure.

Contribution

It offers the first complete classification of level two algebras in multiple algebraic varieties, expanding the understanding of algebraic hierarchy.

Findings

Classified all level two algebras in Jordan, Lie, and associative varieties.

Identified structural properties unique to level two algebras.

Provided a framework for analyzing algebraic levels in finite-dimensional algebras.

Abstract

This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.