Every Leibniz algebra has a maximal homomorphic image that is a Lie algebra. We classify cyclic Leibniz algebras over an arbitrary field. Such algebras have the 1-dimensional abelian Lie algebra as their maximal Lie quotient. We then give examples of Leibniz algebras whose associated maximal Lie quotients exhaust all 2-dimensional possibilities.
"Leibniz algebras with low-dimensional maximal Lie quotients." Involve 12 (5) 839 - 853, 2019. https://doi.org/10.2140/involve.2019.12.839