Representations and (2,3)-Cohomology of Bol Algebras with Applications

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) -co cycles with coefficients in the adjoint representation. The (2,3)-cohomology group is also applied to study abelian extensions of Bol algebras.