Hopf algebroid symmetry of abstract Frobenius extensions of depth 2

摘要

We study Frobenius 1-cells l in an additive bicategory l satisfying the depth 2 condition. We show that the rings of 2-cells l(2) (l x (ι) over bar, l x (ι) over bar) and l(2)((ι) over bar x l, (ι) over bar x l) can be equipped with dual Hopf algebroid structures. We prove also that a Hopf algebroid appears as the solution of the above abstract symmetry problem if and only if it possesses a two sided non-degenerate integral.