The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex 4-dimensional nilpotent weakly associative, complex 4-dimensional symmetric Leibniz algebras, and complex 5-dimensional nilpotent symmetric Leibniz algebras. In particular, we proved that the variety of complex 4-dimensional symmetric Leibniz algebras has no Vergne–Grunewald–O'Halloran Property (there is an irreducible component formed by only nilpotent algebras), but on the other hand, it has Vergne Property (there are no rigid nilpotent algebras).