The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras

TL;DR

This paper provides a geometric classification of specific 4-dimensional nilpotent algebraic structures, including Lie-Yamaguti, Bol, and compatible Lie algebras, enriching the understanding of their geometric properties.

Contribution

It offers the first comprehensive geometric classification of 4-dimensional nilpotent Lie-Yamaguti, Bol, and compatible Lie algebras, filling a gap in algebraic structure theory.

Findings

Complete classification of 4-dimensional nilpotent Lie-Yamaguti algebras

Complete classification of 4-dimensional nilpotent Bol algebras

Complete classification of 4-dimensional nilpotent compatible Lie algebras

Abstract

The geometric classifications of complex $4$-dimensional nilpotent Lie-Yamaguti algebras, $4$-dimensional nilpotent Bol algebras, and $4$-dimensional nilpotent compatible Lie algebras are given.