Degenerations of Leibniz and anticommutative algebras. (English) Zbl 1477.17020
Summary: We describe all degenerations of three-dimensional anticommutative algebras \(\mathfrak{Acom}_3\) and of three-dimensional Leibniz algebras \(\mathfrak{Leib}_3\) over \(\mathbb{C}\). In particular, we describe all irreducible components and rigid algebras in the corresponding varieties.
MSC:
| 17A32 | Leibniz algebras |
| 14D06 | Fibrations, degenerations in algebraic geometry |
| 14L30 | Group actions on varieties or schemes (quotients) |
Keywords:
degeneration; rigid algebra; orbit closure; anticommutative algebra; Leibniz algebra; Lie algebraReferences:
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