Degenerations of binary Lie and nilpotent Malcev algebras

TL;DR

This paper classifies how four-dimensional binary Lie algebras and five- and six-dimensional nilpotent Malcev algebras over complex numbers can degenerate, detailing the structure of their algebraic varieties.

Contribution

It provides a comprehensive description of degenerations and irreducible components of these algebraic structures, extending understanding of their geometric and algebraic properties.

Findings

Complete classification of degenerations for the specified algebras.

Identification of all irreducible components of the algebraic varieties.

Insights into the geometric structure of these algebraic varieties.

Abstract

We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over \mathbb{C}. In particular, we describe all irreducible components of these varieties.