  Dirichlet branes are objects whose transverse coordinates in space are
matrix-valued functions. This leads to considering a matrix algebra or, more
generally, a Lie algebra, as the classical phase space of a certain dynamics
where the multiplication of coordinates, being given by matrix multiplication,
is nonabelian. Further quantising this dynamics by means of a star-product
introduces noncommutativity (besides nonabelianity) as a quantum h-deformation.
The algebra of functions on a standard Poisson manifold is replaced with the
universal enveloping algebra of the given Lie algebra. We define generalised
Poisson brackets on this universal enveloping algebra, examine their
properties, and conclude that they provide a natural framework for dynamical
setups (such as coincident Dirichlet branes) where coordinates are
matrix-valued, rather than number-valued, functions.
