3-form Yang-Mills based on 2-crossed modules

In this paper, we study the higher Yang-Mills theory in framework of gauge theory. It was shown that 2-form electromagnetism can be generalized to with group U(1) replaced by a crossed module Lie groups. To extend even structure, develop 3-form 2-crossed First, give an explicit construction non-degenerate symmetric G-invariant forms on algebras. Then, derive 3-Bianchi-Identities for 3-curvatures. Finally, create action and obtain corresponding field equations.