Structure Constants for New Infinite-Dimensional Lie Algebras of U(N+,N-) Tensor Operators and Applications

TL;DR

This paper introduces new infinite-dimensional Lie algebras based on structure constants for functions on pseudo-unitary group manifolds, extending known algebras like Virasoro and W_ to higher dimensions with applications in field theories and non-commutative geometry.

Contribution

It provides explicit structure constants for these generalized algebras, connecting them to volume-preserving diffeomorphisms and higher-spin tensor operators, expanding the mathematical framework for higher-dimensional symmetries.

Findings

Generalization of Virasoro and W_ algebras to higher dimensions

Explicit structure constants for Moyal brackets on pseudo-unitary group manifolds

Applications to higher-dimensional integrable field theories and non-commutative spaces

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_\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.