A note on maximality of analytic crossed products

Let G be a compact abelian group with the totally ordered dual group Gˆ which admits the positive semigroup Gˆ +. Let N be a von Neumann algebra and α = {αgˆ}gˆ∈Gˆ be an automorphism group of Gˆ on N. We denote N α Gˆ + to the analytic crossed product determined by N and α. We show that if N α Gˆ + is a maximal σ-weakly closed subalgebra of N α Gˆ , then Gˆ + induces an archimedean order in Gˆ .  2005 Elsevier Inc. All rights reserved