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Central extensions of 4-dimensional binary Lie algebras. (English) Zbl 07274818
Summary: 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 \(\mathfrak{CD}\)-algebras of dimensions either \(3\) or \(4\) is also given.

MSC:
17A30 Nonassociative algebras satisfying other identities
17A60 Structure theory for nonassociative algebras
17D10 Mal’tsev rings and algebras
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