Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 4
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, Xin 2016. Operator Algebras and Applications.


    Li, Xin 2016. On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II. Advances in Mathematics, Vol. 291, p. 1.


    Giordano, Thierry and Sierakowski, Adam 2014. Purely infinite partial crossed products. Journal of Functional Analysis, Vol. 266, Issue. 9, p. 5733.


    Li, Xin 2014. On K-theoretic invariants of semigroup C*-algebras attached to number fields. Advances in Mathematics, Vol. 264, p. 371.


    ×
  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 154, Issue 1
  • January 2013, pp. 119-126

The primitive ideal space of the C*-algebra of the affine semigroup of algebraic integers

  • SIEGFRIED ECHTERHOFF (a1) and MARCELO LACA (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004112000485
  • Published online: 01 October 2012
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 RR× over R and as a full corner of a crossed product C0() ⋊ KK*, 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 KK* 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 KK* 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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[7]J. M. G. Fell The dual spaces of C*-algebras. Trans. Amer. Math. Soc. 94 (1960), 365403.

[8]E. Guentner, N. Higson and S. Weinberger The Novikov conjecture for linear groups. Publ. Math. Inst. Hautes Études Sci. 101 (2005), 243268.

[9]E. C. Gootman and J. Rosenberg The structure of crossed product C*-algebras: a proof of the generalized Effros–Hahn conjecture. Invent. Math. 52 (1979), no. 3, 283298.

[10]P. Green The local structure of twisted covariance algebras. Acta Math. 140 (1978), no. 3-4, 191250.

[11]M. Laca and I. Raeburn The ideal structure of the Hecke C*-algebra of Bost and Connes. Math. Ann. 318 (2000), 433451.

[12]M. Laca and I. Raeburn Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers. Adv. Math. 225 (2010), 643688.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×