  Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure
underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi
three-dimensional Lie algebras are classified here. Two types of algebras are
obtained: Six-dimensional Lie algebras that can be considered extension of
semi-Abelian four-dimensional Drinfeld double and unique extensions of
non-Abelian Bianchi algebras. For all of the algebras explicit forms of
generalized frame fields are given.
