The graphical calculus for ribbon categories: Algebras, modules, Nakayama automorphisms

Some graphical aspects of Frobenius structures

“…In (Fuchs 2006) it is further graphically shown, that the Nakayama automorphism α = β l β r is actually an algebra automorphism. Compare this form of α with the form for α given in (3-17) which does not use the closed structure or the braid.…”

“…A main characterization of a Frobenius algebra in theorem 3.6, and one which generalizes, is given by the Frobenius isomorphism A A ∼ = A A * of the left A -modules. The Frobenius bilinear form and its dual allow us to construct such morphisms together with the closed structures (Fuchs 2006, Fuchs & Stigner 2008. We define left/right module maps β r ∈ Hom(A, A * ) , β l ∈ Hom(A, * A) and their inverses.…”