Symmetries of Yang--Mills type polynomial equations (Q1878527)

The author studies geometric symmetries of systems of Euler-Lagrange equations for polynomial Lagrangians of \(L=L(F_{\mu\nu})\) type which are given by means of some basic polynomials. Here \(F_{\mu\nu}\) are the components of curvature form. In the paper it is proved that in this class of equations the classical system of Yang-Mills equations possesses the widest group of symmetry, in particular, symmetry with respect to conformal transforms.