We show that for any expanding map $\phi: T^p\to T^p$, there is an
orientation-preserving self-diffeomorphism of $\RR^{p+2}$ realizing a
hyperbolic attractor derived from $\phi$. The construction is based on a result
in differential topology that for the standard unknotted embedding
$\imath_p:T^p\to\RR^{p+2}$, the subgroup $E_{\imath_p}$ of
$\Aut(T^p)\cong\SL(p,\ZZ)$ which consists of automorphisms that extend over
$\RR^{p+2}$ as orientation-preserving diffeomorphisms, has index at most
$2^p-1$.