Scaling Yetter–Drinfeld Modules

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

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

Answer

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