On the Classification of One Class of Three-Dimensional Bol Algebras with Solvable Enveloping Lie Algebras of Small Dimension Part I

We give the classification of 3-dimensional Bol algebras associated to the trilinears operations $(e_2,e_3,e_2)=e_1,(e_2,e_3,e_3)={\text{pme}}_2$. It turn that for such trilinears operation there exist up to isomorphism and isotopy one family and one exceptional Bol algebras. We describe their corresponding 3-webs.