Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2

Details Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2 Hopf Algebroid Symmetry of Abstract Frobenius Extensions of Depth 2

2003-05-09

arxiv.org/abs/math/0305136v1

Comm. Algebra 32 (11) (2004) 4433 - 4464

Mathematics

Quantum Algebra

23 pages LaTeX2e file with 25 small figures

Scientific paper

We study Frobenius 1-morphisms $\i$ in an additive bicategory $\c$ satisfying the depth 2 condition. We show that the 2-endomorphism rings $\c^2(\i\x\ib,\i\x\ib)$ and $\c^2(\ib\x\i,\ib\x\i)$ 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.

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