# Scaling Yetter–Drinfeld Modules

A braided vector space is a pair $$(V,σ)(V,\sigma)$$ consisting of a vector space $$VV$$, and a linear map $$σ:V⊗V→V⊗V\sigma:V \otimes V \to V \otimes V$$, satisfying the Yang–Baxter equation. Ee can scale the braiding by $$λ∈C\lambda \in \mathbb{C}$$ to produce a new braiding $$λσ\lambda \sigma$$.

Given a Yetter–Drinfeld module $$(V,∙,δ)(V,\bullet,\delta)$$, a braiding is given by
$$σ:V⊗V→V⊗V, v⊗w↦v(−1)∙w⊗v(0). \sigma: V \otimes V \to V \otimes V, ~~~~~~~ v \otimes w \mapsto v_{(-1)}\bullet w \otimes v_{(0)}.$$
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 $$(V,∙,δ)(V,\bullet,\delta)$$ so that its asociated braiding is $$λσ\lambda \sigma$$?

## Answer

Attribution
Source : Link , Question Author : Nadia SUSY , Answer Author : Community