arXiv subjects

Sriwulan Adji

Publications and source records attributed to Sriwulan Adji.

2 recordsLinked to original sources

arXiv2015

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

Let $Γ^{+}$ be the positive cone in a totally ordered abelian group $Γ$, and $α$ an action of $Γ^{+}$ by extendible endomorphisms of a $C^{\ast}$-algebra $A$. Suppose $I$ is an extendible $α$-invariant ideal of $A$. We prove that the partial-isometric crossed product $\mathcal{I}:=I\times_α^{\textrm{piso}}Γ^{+}$ embeds naturally as an ideal of $A\times_α^{\textrm{piso}}Γ^{+}$, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal $\mathcal{I}$ together with the kernel of a natural homomorphism $ϕ: A\times_α^{\textrm{piso}}Γ^{+}\rightarrow A\times_α^{\textrm{iso}}Γ^{+}$ gives a composition series of ideals of $A\times_α^{\textrm{piso}}Γ^{+}$ studied by Lindiarni and Raeburn.

math.OA↗

arXiv2013

The Partial-Isometric Crossed Products by Semigroups of Endomorphisms as Full Corners

Suppose $Γ^{+}$ is the positive cone of a totally ordered abelian group $Γ$, and $(A,Γ^{+},α)$ is a system consisting of a $C^*$-algebra $A$, an action $α$ of $Γ^{+}$ by extendible endomorphisms of $A$. We prove that the partial-isometric crossed product $A\times_α^{\piso}Γ^{+}$ is a full corner in the subalgebra of $Ł(\ell^{2}(Γ^{+},A))$, and that if $α$ is an action by automorphisms of $A$, then it is the isometric-crossed product $(B_{Γ^{+}}\otimes A)\times^{\iso}Γ^{+}$, which is therefore a full corner in the usual crossed product of system by a group of automorphisms. We use these realizations to identify the ideal of $A\times_α^{\piso}Γ^{+}$ such that the quotient is the isometric crossed product $A\times_α^{\iso}Γ^{+}$.

math.OA↗