فهرست نشریات علمی دسترسی آزاد ایران

For a discrete group $\Gamma$, a Hopf von Neumann algebra $(\mathfrak{M},\Delta)$ and a $W^*$-dynamical system $(\mathfrak{M},\Gamma,\alpha)$ such that $(\alpha_s\otimes\alpha_s)\circ\Delta=\Delta\circ\alpha_s$, we show that the crossed product $\mathfrak{M}\rtimes_\alpha\Gamma$ with a co-multiplication is a Hopf von Neumann algebra.Furthermore, we prove that the inner amenability of the predual $\mathfrak{M}_*$ is equivalent to the inner amenability of $(\mathfrak{M}\rtimes_\alpha\Gamma)_*$. Finally, we conclude that if the action $\alpha:\Gamma\rightarrow\mathrm{Aut}(\ell^\infty(\Gamma))$ is defined by $\alpha_s(f)(t)=f(s^{-1}ts)$, then the inner amenability of discrete group $\Gamma$ is equivalent to the inner amenability of $(\ell^\infty(\Gamma)\rtimes_\alpha\Gamma)_*$.