Structure constants for the new infinite-dimensional lie algebras of U(N+,N-)] tensor operators and applications

Abstract

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 W1 algebras to higher dimensions. The connection with volumepreserving 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.