Some graphical aspects of Frobenius structures

Details Some graphical aspects of Frobenius structures Some graphical aspects of Frobenius structures

2012-02-28

arxiv.org/abs/1202.6380v1

Mathematics

Rings and Algebras

to appear in `Categorical information flow in physics and linguistics', E. Grefenstette, Ch. Heunen, and M. Sadrzadeh eds

Scientific paper

We survey some aspects of Frobenius algebras, Frobenius structures and their relation to finite Hopf algebras using graphical calculus. We focus on the `yanking' moves coming from a closed structure in a rigid monoidal category, the topological move, and the `yanking' coming from the Frobenius bilinear form and its inverse, used e.g. in quantum teleportation. We discus how to interpret the associated information flow. Some care is taken to cover non-symmetric Frobenius algebras and the Nakayama automorphism. We review graphically the Larson-Sweedler-Pareigis theorem showing how integrals of finite Hopf algebras allow to construct Frobenius structures. A few pointers to further literature are given, with a subjective tendency to graphically minded work.

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