  A key symmetry of classical $p$-branes is invariance under worldvolume
diffeomorphisms. Under the assumption that the worldvolume, at fixed values of
the time, is a compact, quantisable K\"ahler manifold, we prove that the Lie
algebra of volume-preserving diffeomorphisms of the worldvolume can be
approximated by $su(n)$, for $n\to\infty$. We also prove, under the same
assumptions regarding the worldvolume at fixed time, that classical Nambu
brackets on the worldvolume are quantised by the multibrackets corresponding to
cocycles in the cohomology of the Lie algebra $su(n)$.
