THE COMPOSITION SERIES OF IDEALS OF THE PARTIAL-ISOMETRIC CROSSED PRODUCT BY SEMIGROUP OF ENDOMORPHISMS
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Let Г + be the positive cone in a totally ordered abelian group Γ, and α an action of Г+ 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 ×piso α Г+ embeds naturally as an ideal of A× piso α Г+, 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 Ø : A× piso α + → A × piso α Г+ gives a composition series of ideals of A ×piso α Г+ studied by Lindiarni and Raeburn.
Abstract
Let Г + be the positive cone in a totally ordered abelian group Γ, and α an action of Г+ 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 ×piso α Г+ embeds naturally as an ideal of A× piso α Г+, 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 Ø : A× piso α + → A × piso α Г+ gives a composition series of ideals of A ×piso α Г+ studied by Lindiarni and Raeburn.
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