Hopf algebroids and H-separable extensions

Lars Kadison
2002 Proceedings of the American Mathematical Society  
Since an H-separable extension A|B is of depth two, we associate to it dual bialgebroids S := End B A B and T := (A ⊗ B A) B over the centralizer R as in Kadison-Szlachányi. We show that S has an antipode τ and is a Hopf algebroid. T op is also Hopf algebroid under the condition that the centralizer R is an Azumaya algebra over the center Z of A. For depth two extension A|B, we show that End A A ⊗ B A ∼ = T End B A.
doi:10.1090/s0002-9939-02-06876-4 fatcat:v5ewfkqwdbdivhpg4q4eljswfa