  The structure constants for Moyal brackets of an infinite basis of functions
on the algebraic manifolds M of pseudo-unitary groups U(N_+,N_-) are provided.
They generalize the Virasoro and W_\infty algebras to higher dimensions. The
connection with volume-preserving diffeomorphisms on M, higher generalized-spin
and tensor operator algebras of U(N_+,N_-) is discussed. These
centrally-extended, infinite-dimensional Lie-algebras provide also the arena
for non-linear integrable field theories in higher dimensions, residual gauge
symmetries of higher-extended objects in the light-cone gauge and C^*-algebras
for tractable non-commutative versions of symmetric curved spaces.
