The primitive ideal space of the C*-algebra of the affine semigroup of algebraic integers
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Bibliographic record
Abstract
Abstract The purpose of this paper is to give a complete description of the primitive ideal space of the C*-algebra [ R ] associated to the ring of integers R in a number field K in the recent paper [ 5 ]. As explained in [ 5 ], [ R ] can be realized as the Toeplitz C*-algebra of the affine semigroup R ⋊ R × over R and as a full corner of a crossed product C 0 ( ) ⋊ K ⋊ K *, where is a certain adelic space. Therefore Prim( [ R ]) is homeomorphic to the primitive ideal space of this crossed product. Using a recent result of Sierakowski together with the fact that every quasi-orbit for the action of K ⋊ K * on contains at least one point with trivial stabilizer we show that Prim( [ R ]) is homeomorphic to the quasi-orbit space for the action of K ⋊ K * on , which in turn may be identified with the power set of the set of prime ideals of R equipped with the power-cofinite topology.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.004 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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