“School of Mathematics”
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| Paper IPM / M / 18013 | ||||||||||||||||||
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or a discrete group Γ, a Hopf von Neumann algebra (M,Δ)
and a W∗-dynamical system (M,Γ,α)
such that
(αs⊗αs)∘Δ=Δ∘αs, we show that the crossed product
M⋊ 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)_*.
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