Infinite-dimensional gauge groups and special nonlinear gravitons (Q1184391)

This paper is concerned with the interplay between certain completely integrable differential equations and their associated Lie algebras, and Yang-Mills equations in four dimensions. If the dimension of the Lie algebra is allowed to approach infinity in some sense, such as an algebra of vector fields, there results a self-dual metric, i.e., a non-linear graviton. In one case the metric turns out to be flat, leading to a solution of the original equations by means of a coordinate transformation.