Structure Constants for New Infinite - Dimensional Lie Algebras of

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 ∞ 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.