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

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.