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

2026/07/23 by Saeid Zahmatkesh
Mathematics · #math.OA

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Abstract

For an odd prime p, we consider an action α of the semigroup ℕ² on the algebra C(ℤ_p) induced by the multiplication on the compact topological ring of p-adic integers ℤ_p. We then identify all primitive ideals of the partial-isometric crossed product C(ℤ_p)\rtimes_α^\textrmpiso ℕ² and describe the hull-kernel closures of the subsets of its primitive ideal space.

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