Some properties of factorizable Hopf algebras

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On higher Frobenius-Schur indicators (2003, background): “.2 If R 21 arises from Rby interchanging the tensorands, then the map Φ : D(H)∗ → D(H), ψ→ (id⊗ψ)(R 21R) is bijective, i.e., the Drinfel’d double is factorizable (cf. [33], Def. 2.1, p. 543; see also [37], p. 1892). If restricted to the character ring of D(H), Φ induces an algebra isomorphism betwee”
An analogue of Radford's S4 formula for finite tensor categories (2004, methodology): “Thus to specify a morphism A → A ∗∗ in C⊠C op is the same as to specify a collection of morphisms ψi : ∗ Li → ∗∗∗∗∗ Li in C. Recall [Mu, ENO] that for any simple object L in C one defines its squared norm |L| 2 as follows: choose an isomorphism φ : L → L ∗∗ (such an isomorphism always exists and is ”