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).
Categories: math.RA