  Superimposed D-branes have matrix-valued functions as their transverse
coordinates, since the latter take values in the Lie algebra of the gauge group
inside the stack of coincident branes. This leads to considering a classical
dynamics where the multiplication law for coordinates and/or momenta, being
given by matrix multiplication, is nonabelian. Quantisation further introduces
noncommutativity as a deformation in powers of Planck's constant. Given an
arbitrary simple Lie algebra and an arbitrary Poisson manifold, both
finite-dimensional, we define a corresponding C*-algebra that can be regarded
as a nonabelian Poisson manifold. The latter provides a natural framework for a
matrix-valued classical dynamics.
