## 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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