Simple ω-Lie Algebras and 4-Dimensional ω-Lie Algebras Over C

In this paper, we study simple omega-Lie algebras and 4-dimensional omega-Lie algebras over the field of complex numbers. We provide an approach to classify all 4-dimensional non-Lie complex-Lie algebras. We prove that any non-Lie finite-dimensional simple-Lie algebra has dimension 3. A complete list of all non-Lie complex simple omega-Lie algebras is also derived.