On solutions of the Yang-Mills equations in the algebra of h-forms

Abstract

Abstract We study the Yang-Mills equations in the algebra of h-forms, which is developed in the works of N. G. Marchuk and the author. The algebra of h-forms is a special geometrization of the Clifford algebra and is a generalization of the Atiyah-K¨ahler algebra. We discuss an invariant subspace of the constant Yang-Mills operator in the algebra of h-forms and present particular classes of solutions of the Yang-Mills equations.