Szeto, George; Xue, Lianyong On Hopf Galois Hirata extensions. (English) Zbl 1034.16041 Int. J. Math. Math. Sci. 2003, No. 64, 4033-4039 (2003). Summary: Let \(H\) be a finite-dimensional Hopf algebra over a field \(k\), \(H^*\) the dual Hopf algebra of \(H\), and \(B\) a right \(H^*\)-Galois and Hirata separable extension of \(B^H\). Then \(B\) is characterized in terms of the commutator subring \(V_B(B^H)\) of \(B^H\) in \(B\) and the smash product \(V_B(B^H)\#H\). A sufficient condition is also given for \(B\) to be an \(H^*\)-Galois Azumaya extension of \(B^H\). MSC: 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) Keywords:finite-dimensional Hopf algebras; Hirata separable extensions; Galois Azumaya extensions; smash products PDFBibTeX XMLCite \textit{G. Szeto} and \textit{L. Xue}, Int. J. Math. Math. Sci. 2003, No. 64, 4033--4039 (2003; Zbl 1034.16041) Full Text: DOI EuDML