Central extensions of 4-dimensional binary Lie algebras

Abstract

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 $3$ or $4$. From here, a classification of central extensions of complex non-Lie anticommutative $\mathfrak{ℭ}\mathfrak{𝔇}$-algebras of dimensions either $3$ or $4$ is also given.