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Homology and central extensions of Leibniz and Lie \(n\)-algebras. (English) Zbl 1287.17004

Summary: From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz \(n\)-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie \(n\)-algebras. We also consider the relative case: homology of Leibniz \(n\)-algebras relative to the subvariety of Lie \(n\)-algebras.

MSC:

17A42 Other \(n\)-ary compositions \((n \ge 3)\)
17A32 Leibniz algebras
18E99 Categorical algebra
18G10 Resolutions; derived functors (category-theoretic aspects)
18G50 Nonabelian homological algebra (category-theoretic aspects)
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