Some graphical aspects of Frobenius structures

Abstract

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.