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We go on with the program started in the companion paper [CDI+] of defining aPoisson bracket structure on the space of solutions of the equations of motionof first order Hamiltonian field theories. The case of non-Abelian gaugetheories is addressed by using a suitable version of the coisotropic embeddingtheorem.

The Geometry of the solution space of first order Hamiltonian field theories II: non-Abelian gauge theories