INNER AMENABILITY OF CERTAIN LAU ALGEBRAS ASSOCIATED TO DISCRETE CROSSED PRODUCTS

Abstract

For a discrete group Γ, a Hopf von Neumann algebra (M, ∆) and a W*-dynamical system (M, Γ, α) such that (Formula Presented)), we show that the crossed product M ⋊α Γ with a comultiplication is a Hopf von Neumann algebra. Furthermore, we prove that the inner amenability of the predual M* is equivalent to the inner amenability of (M ⋊α Γ)*. Finally, we conclude that if the action α: Γ → Aut(ℓ∞(Γ)) is defined by αs(f)(t) = f(s−1ts), then the inner amenability of discrete group Γ is equivalent to the inner amenability of (ℓ∞(Γ) ⋊α Γ)*. © 2024 Iranian Mathematical Society.