Exponential solutions of euler-lagrange equations for field of linear frames in nonlinear model of born-infeld type

We investigate a model of the field of linear frames on the product manifold M = ℝ × G, where G is a semisimple Lie group. The model is invariant under the natural action of the group GL(n, ℝ) (n = dim M). It results in a modified Born-Infeld-type nonlinearity of field equations.We find two families of solutions of the Euler-Lagrange equations. The solutions are bases for the Lie algebra of left-invariant vector fields on ℝ × G “deformed” by a GL(n, ℝ)-valued mapping of the exponential form.