Hopf algebroids and H-separable extensions

摘要

Since an H-separable extension AB is of depth two, we associate to it dual bialgebroids S := End (B)A(B) and T := (Acircle times(B)A)(B) over the centralizer R as in Kadison-Szlachanyi. We show that S has an antipode tau 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 AB, we show that End (A)Acircle times(B)A congruent to T x End (B)A. [References: 22]