The composition series of ideals of the partial-isometric crossed product by semigroup of endomorphisms

الأصل · EN

Let Γ⁺ be the positive cone in a totally ordered abelian group Γ, and α an action of Γ⁺ by extendible endomorphisms of a C-algebra A. Suppose I is an extendible α-invariant ideal of A. We prove that the partial-isometric crossed product I:=I×αpisoΓ⁺ embeds naturally as an ideal of A×αpisoΓ⁺, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal I together with the kernel of a natural homomorphism ϕ: A×αpisoΓ⁺→ A×αisoΓ⁺ gives a composition series of ideals of A×αpisoΓ⁺ studied by Lindiarni and Raeburn.