The class of binary Lie algebras contains the one of Malcev algebras (and so the one of Lie algebras). We provide a classification of central extensions of complex non-Malcev binary Lie algebras of dimensions either or . From here, a classification of central extensions of complex non-Lie anticommutative -algebras of dimensions either or is also given.
Hani Abdelwahab. Antonio J. Calderón Martín. Amir Fernández Ouaridi. "Central extensions of 4-dimensional binary Lie algebras." Rocky Mountain J. Math. 50 (5) 1541 - 1559, October 2020. https://doi.org/10.1216/rmj.2020.50.1541