The Primitive Ideal Space of the Partial-isometric Crossed Product by Automorphic Actions of the Semigroup N
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Journal article
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Strategic Research Themes
Publication Details
Author list: Saeid Zahmatkesh
Publisher: Mathematical Society of the Rep. of China
Publication year: 2024
Journal acronym: Taiwanese J. Math.
Volume number: 28
Issue number: 3
Start page: 493
End page: 516
Number of pages: 24
ISSN: 10275487
Languages: English-United States (EN-US)
Abstract
Let $(A,\mathbb{N}^{2},\alpha)$ be a dynamical system consisting of a $C^*$-algebra $A$ and an action $\alpha$ of $\mathbb{N}^{2}$ on $A$ by automorphisms. Let $A\times_{\alpha}^{\textrm{piso}}\mathbb{N}^{2}$ 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.
Keywords
C*-algebra, automorphism, crossed product, partial isometry, primitive ideal
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