The geometric classification of Leibniz algebras

preprint2021arXivOpen access

Abstract

We describe all rigid algebras and all irreducible components in the variety of four dimensional Leibniz algebras Leib4\mathfrak{Leib}_4 over C.\mathbb{C}. In particular, we prove that the Grunewald--O'Halloran conjecture is not valid and the Vergne conjecture is valid for Leib4.\mathfrak{Leib}_4.

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