  We show which $H^{op}$-cleft extensions $k#_\sigma H^{op}$ of the base field
$k$ for a dual quasitriangular Hopf algebra $(H, r)$ are $H$-Azumaya. The
result is given in terms of bijectivity of a map $\theta_\sigma\colon H\to H^*$
defined in terms of $r$ and the 2-cocycle $\sigma$, generalizing a well-known
result for the commutative and cocommutative case. We illustrate the Theorem
with an explicit computation for the Hopf algebras of type E(n).
