On Bol algebras

In this paper Bol algebras are considered. These algebras are related to fiber spaces in geometry and can be viewed as Lie triple systems with an additional bilinear anticommutative operation that satisfies some supplementary conditions. In the paper Bol algebras are approached through Lie algebras and the ones considered here are connected with the three-dimensional solvable Lie triple system. par Since the Bol algebras considered have dimension 3, their canonical enveloping Lie algebras have dimension less than or equal to 6. In the paper, only Bol algebras of dimension 3, with the trilinear operation of type II ((e_2,e_3,e_3)=e_1) and with a canonical enveloping Lie algebra of dimension 4 and 5 are considered. In the first case, all algebras with the mentioned conditions are classified up to isomorphism and up to isotopy. In the case of Bol algebras with an enveloping Lie algebra of dimension 5, their classification, up to isomorphism, is obtained.