\lambda_{0n}(t) \lambda^{-1}$, $t \in \RR$, for some $\lambda \in {\mbox{SO$_0(2,n\!-\!1)$}}$ generate admissible geodesic worldlines in the sense just indicated. These worldlines are closed, timelike curves, whose causal completion is the entire space ${\mbox{{AdS}$^n\,$}}$. Hence, the maximal laboratory localization region $W$ for such geodesic observers must be the entire space-time, ${\mbox{{AdS}$^n\,$}}$. For uniformly accelerated observers, the corresponding one-parameter subgroups are of the form $\lambda \lambda_{01}(t) \lambda^{-1}$, $t\in\RR$, for some $\lambda\in{\mbox{SO$_0(2,n\!-\!1)$}}$. Their laboratory regions, called AdS wedges, are described immediately below. The algebras $\As(W)$ corresponding to any such wedge region as well as to $W = {\mbox{{AdS}$^n\,$}}$ are taken to be weakly closed.

We define a “wedge” in to be the causal completion of the worldline of a uniformly accelerated observer in . To be concrete and in order to simplify the necessary computations, we consider the particular choice of region $$W_R = \{ x \in {\mbox{{AdS}$^n\,$}}\mid x_1 > |x_0|\, , x_n > 0 \} \, ,$$ on which the one-parameter subgroup of boosts $\lambda_{01}(t)$, $t\in\RR$, in the $0$–$1$–plane acts in an orthochronous manner. For any $x_O \in W_R$, the curve $t \mapsto \lambda_{01}(t) x_O$ is the worldline of a uniformly accelerated observer for which the causal completion is precisely $W_R$. By 