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Let $A \subseteq E$ be an extension of Hopf algebras such that there exists anormal left $A$-module coalgebra map $\pi : E \to A$ that splits the inclusion.We shall describe the set of all coquasitriangular structures on the Hopfalgebra $E$ in terms of the datum $(A, E, \pi)$ as follows: first, any suchextension $E$ is isomorphic to a unified product $A \ltimes H$, for someunitary subcoalgebra $H$ of $E$ (\cite{am2}). Then, as a main theorem, weestablish a bijective correspondence between the set of all coquasitriangularstructures on an arbitrary unified product $A \ltimes H$ and a certain set ofdatum $(p, \tau, u, v)$ related to the components of the unified product. Asthe main application, we derive necessary and sufficient conditions for Majid'sinfinite dimensional quantum double $D_{\lambda}(A, H) = A \bowtie_{\tau} H$ tobe a coquasitriangular Hopf algebra. Several examples are worked out in detail.

Coquasitriangular structures for extensions of Hopf algebras. Applications