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Saeid Zahmatkesh

Publications and source records attributed to Saeid Zahmatkesh.

9 recordsLinked to original sources
arXiv2026

The primitive ideal space of the partial-isometric crossed product corresponding to an action induced by the multiplication on $p$-adic integers

For an odd prime $p$, we consider an action $α$ of the semigroup $\mathbb{N}^{2}$ on the algebra $C(\mathbb{Z}_p)$ induced by the multiplication on the compact topological ring of $p$-adic integers $\mathbb{Z}_p$. We then identify all primitive ideals of the partial-isometric crossed product $C(\mathbb{Z}_{p})\rtimes_α^{\textrm{piso}} \mathbb{N}^{2}$ and describe the hull-kernel closures of the subsets of its primitive ideal space.

math.OA↗
arXiv2023

The primitive ideal space of the partial-isometric crossed product by automorphic actions of the semigroup $\mathbb{N}^{2}$

Let $(A,\mathbb{N}^{2},α)$ be a dynamical system consisting of a $C^*$-algebra $A$ and an action $α$ of $\mathbb{N}^{2}$ on $A$ by automorphisms. Let $A\times_α^{\textrm{piso}}\mathbb{N}^{2}$ be the partial-isometric crossed product of the system. We apply the fact that it is a full corner of a crossed product by the group $\mathbb{Z}^{2}$ in order to give a complete description of its primitive ideal space.

math.OA↗
arXiv2023

The composition series of ideals of the partial-isometric crossed product by the semigroup $\mathbb{N}^{2}$

Suppose that $α$ is an action of the semigroup $\mathbb{N}^{2}$ on a $C^*$-algebra $A$ by endomorphisms. Let $A\times_α^{\textrm{piso}} \mathbb{N}^{2}$ be the associated partial-isometric crossed product. By applying an earlier result which embeds this semigroup crossed product (as a full corner) in a crossed product by the group $\mathbb{Z}^{2}$, a composition series $0\leq L_{1}\leq L_{2}\leq A\times_α^{\textrm{piso}} \mathbb{N}^{2}$ of essential ideals is obtained for which we identify the subquotients with familiar algebras.

math.OA↗
arXiv2022

Partial-isometric crossed products of dynamical systems by left LCM semigroups

Let P be a left LCM semigroup, and $α$ an action of $P$ by endomorphisms of a $C^{*}$-algebra $A$. We study a semigroup crossed product $C^{*}$-algebra in which the action $α$ is implemented by partial isometries. This crossed product gives a model for the Nica-Teoplitz algebras of product systems of Hilbert bimodules (associated with semigroup dynamical systems) studied first by Fowler, for which we provide a structure theorem as it behaves well under short exact sequences and tensor products.

math.OA↗
arXiv2021

The Nica-Toeplitz algebras of dynamical systems over abelian lattice-ordered groups as full corners

Consider the pair $(G,P)$ consisting of an abelian lattice-ordered discrete group $G$ and its positive cone $P$. Let $α$ be an action of $P$ by extendible endomorphisms of a $C^*$-algebra $A$. We show that the Nica-Toeplitz algebra $\mathcal{T}_{\textrm{cov}}(A\times_α P)$ is a full corner of a group crossed product $\mathcal{B}\rtimes_βG$, where $\mathcal{B}$ is a subalgebra of $\ell^{\infty}(G,A)$ generated by a collection of faithful copies of $A$, and the action $β$ on $\mathcal{B}$ is given by the shift on $\ell^{\infty}(G,A)$. By using this realization, we show that the ideal $\mathcal{I}$ of $\mathcal{T}_{\textrm{cov}}(A\times_α P)$ for which the quotient algebra $\mathcal{T}_{\textrm{cov}}(A\times_α P)/\mathcal{I}$ is the isometric crossed product $A\times_α^{\textrm{iso}} P$ is also a full corner in an ideal $\mathcal{J}\rtimes_βG$ of $\mathcal{B}\rtimes_βG$.

math.OA↗
arXiv2017

The partial-isometric crossed products by semigroups of endomorphisms are Morita equivalent to crossed products by groups

Let $Γ^{+}$ be the positive cone of a totally ordered abelian discrete group $Γ$, and $α$ an action of $Γ^{+}$ by extendible endomorphisms of a $C^*$-algebra $A$. We prove that the partial-isometric crossed product $A\times_α^{\textrm{piso}}Γ^{+}$ is a full corner of a group crossed product $\mathcal{B}\times_βΓ$, where $\mathcal{B}$ is a subalgebra of $\ell^{\infty}(Γ,A)$ generated by a collection of faithful copies of $A$, and the action $β$ on $\mathcal{B}$ is induced by shift on $\ell^{\infty}(Γ,A)$. We then use this realization to show that $A\times_α^{\textrm{piso}}Γ^{+}$ has an essential ideal $J$, which is a full corner in an ideal $\mathcal{I}\times_βΓ$ of $\mathcal{B}\times_βΓ$.

math.OA↗
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↗