$3$-dimensional Bol loops corresponding to solvable Lie triple systems

TL;DR

This paper classifies 3-dimensional differentiable Bol loops associated with solvable Lie groups, completing the broader classification of such loops by analyzing their underlying Lie triple systems.

Contribution

It provides a complete classification of 3-dimensional differentiable Bol loops linked to solvable Lie groups using Lie triple systems, extending previous work.

Findings

Complete classification of 3D differentiable Bol loops with solvable Lie groups

Identification of all such loops via solvable Lie triple systems

Extension of prior classification results in the field

Abstract

We classify the connected $3$-dimensional differentiable Bol loops $L$ having a solvable Lie group as the group topologically generated by the left translations of $L$ using $3$-dimensional solvable Lie triple systems. Together with \cite{figula} our results complete the classification of all $3$-dimensional differentiable Bol loops.