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The primitive ideal space of the C*-algebra of the affine semigroup of algebraic integers
- Source :
- Mathematical Proceedings of the Cambridge Philosophical Society. 154:119-126
- Publication Year :
- 2012
- Publisher :
- Cambridge University Press (CUP), 2012.
-
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 C0() ⋊ 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.
- Subjects :
- Pure mathematics
Mathematics::Commutative Algebra
Mathematics::Operator Algebras
Semigroup
General Mathematics
010102 general mathematics
Mathematics - Operator Algebras
Algebraic number field
Primary 46L05, 46L80, Secondary 20Mxx, 11R04
Space (mathematics)
01 natural sciences
Ring of integers
Primitive ideal
Prime (order theory)
Crossed product
0103 physical sciences
FOS: Mathematics
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
010307 mathematical physics
0101 mathematics
Algebraic number
Operator Algebras (math.OA)
GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries)
Mathematics
Subjects
Details
- ISSN :
- 14698064 and 03050041
- Volume :
- 154
- Database :
- OpenAIRE
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Accession number :
- edsair.doi.dedup.....968505e3087c096772301a280872b09b