A braided vector space is a pair (V,σ) consisting of a vector space V, and a linear map σ:V⊗V→V⊗V, satisfying the Yang–Baxter equation. Ee can scale the braiding by λ∈C to produce a new braiding λσ.
Given a Yetter–Drinfeld module (V,∙,δ), a braiding is given by
As above, scaling this braiding again gives a braiding – however it does not come from any obvious rescaling of the Yetter–Drinfeld module. Is their some clever way to scale (V,∙,δ) so that its asociated braiding is λσ?