the assumed covariance, all results concerning this wedge have natural extensions to all images of $W_R$ under . We therefore define the set of wedges to be $$\Ws \doteq \{ \lambda W_R \mid \lambda \in {\mbox{SO$_0(2,n\!-\!1)$}}\} \, .$$ These are maximal laboratory localizations for the uniformly accelerated observers.

We can now describe the four standing assumptions of this paper. A discussion of their physical motivation is given in [@AdS], so we shall only expand upon the less familiar ones.

1.  There exists a strongly continuous, unitary, nontrivial representation $U$ of the symmetry group acting on a separable Hilbert space ${{\cal H}}$.[^3]

2.  On $\Hs$ act the global von Neumann algebra of observables ${{\cal A}}= \As({\mbox{{AdS}$^n\,$}})$, which contains any observable measurable in ${\mbox{{AdS}$^n\,$}}$, and an isotonous family of von Neumann algebras $\wnet$ associated with the wedges $\Ws$. Furthermore, one has $$\label{weakadditivity}
    \bigvee_{W \in \Ws} \As(W) = \As \, .$$

3.  For each wedge $W \in \Ws$ and $\lambda \in {\mbox{SO$_0(2,n\!-\!1)$}}$, one has the equality $$U(\lambda)  {{\cal A}}(W) U(\lambda)^{-1} = {{\cal A}}(\lambda W) \, .$$

The weak additivity condition (\[weakadditivity\]) is a generalization of the natural idea that all observables are constructed out of local ones. But in contrast to [@AdS], we 