  Infinite enlargements of finite pseudo-unitary symmetries are explicitly
provided in this letter. The particular case of u(2,2)=so(4,2)+u(1) constitutes
a (Virasoro-like) infinite-dimensional generalization of the 3+1-dimensional
conformal symmetry, in addition to matter fields with all conformal spins.
These algebras provide a new arena for integrable field models in higher
dimensions; for example, Anti-de Sitter and conformal gauge theories of
higher-so(4,2)-spin fields. A proposal for a non-commutative geometrical
interpretation of space is also outlined.
