Primitive Ideal Space of $C^*(R_+)\rtimes R^\times$ (2408.09863v1)

Abstract: For an integral domain $R$ satisfying certain condition, we characterize the primitive ideal space and its Jacobson topology of the semigroup crossed product $C^*(R_+) \rtimes R^\times$. The main example is when $R=\mathbb{Z}[\sqrt{-3}]$.