Homological invariants in gauge theories

Extending the gauge formalism of the physical field theory to general graded Lie algebras, we show that in this formalism cohomology groups naturally arise, invariant under gauge transformations. Links of these groups to the Chern-Weil theory of characteristic classes are established. Applications of these cohomologies to Gerstenhaber-Nijenhuis deformations and Yang-Mills equations are discussed. These results can also be useful in the theory of integrable evolution equations and geometry of Lie groups.