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

Abstract

For an odd prime $p$, we consider an action $\alpha$ 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 $C({\mathbb{Z}}_p){⋊}_{\alpha }^{\text{piso}}{\mathbb{N}}^2$ and describe the hull-kernel closures of the subsets of its primitive ideal space.

This is the first version (19 pages)