  For a quasi-triangular Hopf algebra $\left( H,R\right) $, there is a notion
of transmuted braided group $H_{R}$ of $H$ introduced by Majid. The transmuted
braided group $H_{R}$ is a Hopf algebra in the braided category
$_{H}\mathcal{M}$. The $R$-adjoint-stable algebra associated with any simple
left $H_{R}$-comodule is defined by the authors, and is used to characterize
the structure of all irreducible Yetter-Drinfeld modules in ${}_{H}^{H}
\mathcal{YD}$. In this note, we prove for a semisimple factorizable Hopf
algebra $ \left( H,R\right) $ that any simple subcoalgebra of $H_R$ is
$H$-stable and the $R$-adjoint-stable algebra for any simple left
$H_R$-comodule is anti-isomorphic to $H$. As an application, we characterize
all irreducible Yetter-Drinfeld modules.
