p-branes from generalized Yang-Mills theory

We consider the reduced, quenched version of a generalized Yang-Mills actio n in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl-Wigner-Moyal correspondence into a field theory ov er a non-commutative phase space. We show that the 'classical' limit of thi s field theory is encoded into the effective action of an open, (4k - 1)-di mensional, bulk brane enclosed by a dynamical, Chern-Simons type, (4k - 2)- dimensional, boundary brane. The bulk action is a pure volume term, while t he boundary action carries all the dynamical degrees of freedom.