The classification of $\omega$-Lie algebras

TL;DR

This paper provides a complete classification of $$-Lie algebras over the complex numbers, addressing an open problem in their structural understanding.

Contribution

It offers the first comprehensive classification of $$-Lie algebras over , expanding the foundational knowledge of their structure.

Findings

Complete classification of $$-Lie algebras over 

Clarification of the structure of $$-Lie algebras

Addresses an open problem in algebraic classification

Abstract

Zusmanovich gave a fundamental result on the structure of $\omega$-Lie algebras. But up to now, the classification of $\omega$-Lie algebras is still open. In this paper, we give a complete classification of $\omega$-Lie algebras over $\mathbb C$.