## On Hopf Galois Hirata extensions.(English)Zbl 1034.16041

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.)
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