Degenerations of Zinbiel and nilpotent Leibniz algebras

TL;DR

This paper classifies how four-dimensional Zinbiel and nilpotent Leibniz algebras over the complex numbers can degenerate, identifying all irreducible components in their algebraic varieties.

Contribution

It provides a complete description of degenerations and irreducible components for these specific algebra classes, advancing understanding of their geometric structure.

Findings

Classification of degenerations for four-dimensional Zinbiel algebras

Classification of degenerations for four-dimensional nilpotent Leibniz algebras

Identification of all irreducible components in their varieties

Abstract

We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over C. In particular, we describe all irreducible components in the corresponding varieties.