Dirichlet branes and a cohomological definition of time flow

Understand

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.