Galois objects over generalized Drinfeld doubles, with an application to \(u_q({\mathfrak sl}_2)\)
The author obtains some general results about Galois objects over twisted tensor products and over normal quotient Hopf algebras. He applies these ideas to the finite Hopf algebra \(u_q({\mathfrak sl}_2)\) when \(q\) is a root of unity. This is a quotient of the Drinfeld double of a Taft algebra by a normal Hopf subalgebra. His methods thus yield all cleft extensions of \(u_q({\mathfrak sl}_2)\). This is a special case of a result of \textit{R. Günther} in his thesis [Univ. München (1998; Zbl 0956.16016)], who used different methods involving the diamond lemma.
scientific article; zbMATH DE number 1340562