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Hopf algebroids and H-separable extensions

Authors:	Lars Kadison

Institution:	Matematiska Institutionen, Göteborg University, S-412 96 Göteborg, Sweden

Abstract:	Since an H-separable extension $A \vert B$ is of depth two, we associate to it dual bialgebroids $S := \operatorname{End}{}_BA_B$ and $T := (A \otimes_B A)^B$ over the centralizer as in Kadison-Szlachányi. We show that has an antipode $\tau$ and is a Hopf algebroid. $T^{\operatorname{op}}$ is also Hopf algebroid under the condition that the centralizer is an Azumaya algebra over the center of . For depth two extension $A \vert B$ , we show that $\operatorname{End}{}_AA\otimes_B A \cong T \ltimes \operatorname{End}{}_BA$ .

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