Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 2 2024 03 01 Inner amenability of certain Lau algebras associated to discrete crossed products 253 260 209686 10.30504/jims.2024.470441.1197 EN M. R. Ghanei Department of Mathematics, Khansar Campus, University of Isfahan, Isfahan, Iran. Journal Article 2024 07 29 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.<br />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 $(\ell^\infty(\Gamma)\rtimes_\alpha\Gamma)_*$. https://jims.ims.ir/article_209686_12bc1810e92b5c94fc9bacb29e67a6fc.pdf