  A representation theory for Bol algebras is proposed. For a suitable
(2,3)-cohomology theory for Bol algebras, we define a (2,3)-coboundary with
companion and next we define a (2,3)-cohomology group. Deformations of Bol
algebras are investigated. In particular, one-parameter infinitesimal
deformations of Bol algebras are characterized in terms of Bol algebras of
deformation type and (2,3)-cocycles with coefficients in the adjoint
representation. The (2,3)-cohomology group is also applied to study abelian
extensions of Bol algebras.
