Degenerations of Leibniz and Anticommutative Algebras

Abstract

AbstractWe describe all degenerations of three-dimensional anticommutative algebras $\mathfrak{A}\mathfrak{c}\mathfrak{o}\mathfrak{m}_{3}$ and of three-dimensional Leibniz algebras $\mathfrak{L}\mathfrak{e}\mathfrak{i}\mathfrak{b}_{3}$ over $\mathbb{C}$. In particular, we describe all irreducible components and rigid algebras in the corresponding varieties.