Parametrization of causal actions of universal covering groups and global hyperbolicity (Q1067230)

\(\tilde G=S\tilde U(1,1)\) obtained as transformation group of the universal covering of the real projective line \(\tilde S_ 1\) is, together with its action on \(\tilde S_ 1\) and its group operations, coordinatized. An analoguous procedure is applied to \(S\tilde U(2,2)\). Extending the earlier result that the pseudo-Riemannian structure on \(\tilde G\) obtained by the invariant bilinear form on the Lie-algebra induces a causal ordering, it is shown that global hyperbolicity does not hold; the causal interval between e and the generator \(\zeta\) of the center of \(\tilde G\) is a maximal globally hyperbolic submanifold.