Structure Constants for 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 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.
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