Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T04:27:29.615Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Stably Projectionless C*-Algebras Arising as Crossed Products

Published online by Cambridge University Press:  20 November 2018

Akitaka Kishimoto  and
Alex Kumjian
Akitaka Kishimoto
Affiliation:
Department of Mathematics Hokkaido University Sapporo 060 Japan email: e-mail: [email protected]. ac.jp
Alex Kumjian
Affiliation:
Department of Mathematics University of Nevada Reno, Nevada 89557 U.S.A. email: e-mail: alex@math. unr. edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

large class of simple stably projectionless C*-algebras are shown to arise as crossed products of simple purely infinite C*-algebras by trace scaling one-parameter automorphism groups. The Elliott invariant is computed for this class.

Keywords

46L35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 5 , 01 October 1996 , pp. 980 - 996
Copyright
Copyright © Canadian Mathematical Society 1996

References

[Bl] Blackadar, B., A simple C*-algebra with no nontrivial projections, Proc. Amer. Math., Soc. 78(1980), 504–508.Google Scholar
[B2] Blackadar, B., K-theoryfor operator algebras, MSRI Publication Series 5, Springer-Verlag, New York, Heidelberg, Berlin, Tokyo, 1986.Google Scholar
[BK] Blackadar, B. and Kumjian, A., Skew products of relations and structure of simple C*-algebras, Math., Z. 189(1985), 55–63.Google Scholar
[BEH] Bratteli, O., Elliott, G.A., and Herman, R.H., On the possible temperatures of a dynamical system, Comm. Math., Phys. 74(1980), 281–285.Google Scholar
[BEK] Bratteli, O., Elliott, G.A., and Kishimoto, A., The temperature state space of a C*-dynamical system, I, Yokohama Math., J. 28(1980), 125–167.Google Scholar
[Col] Connes, A., An analogue of the Thorn isomorphism for crossed products of a C*-algebra by an action of ℝ, Adv. in, Math. 39(1981), 31–55.Google Scholar
[Co2] Connes, A., A survey of foliations and operator algebras. In: Proc. Sympos. Pure Math., (1) 38(1982), 521–628.Google Scholar
[Cul] Cuntz, J., Simple C*-algebras generated by isometries, Comm. Math., Phys 57(1977), 173–185.Google Scholar
[Cu2] Cuntz, J., K-theory for certain C*-algebras, Ann., Math. 113(1981), 181–197.Google Scholar
[Cu3] Cuntz, J., The internal structure of simple C*-algebras. In: Proc. Sympos. Pure Math., (1) 38(1982), 85–115.Google Scholar
|CP] Cuntz, J. and Pedersen, G.K., Equivalence and traces on C* -algebras, J. Funct., Anal. 33(1979), 135–164.Google Scholar
[Ell] Elliott, G.A., private communication, 1980.Google Scholar
[E12] Elliott, G.A., The classification problem for amenable C* -algebras, preprint.Google Scholar
[Ev] Evans, D.E., On 0n, Publ. Res. Inst. Math. Sci., Kyoto, Univ. 16(1980), 915–927.Google Scholar
[G] Green, P., The local structure of twisted covariance algebras, Acta, Math. 140(1978), 191–250.Google Scholar
[Kr] Kirchberg, E., The classification of purely infinite C*-algebras using Kasparov s theory, preprint.Google Scholar
[Ks] Kishimoto, A., Simple crossed products by locally compact abelian groups, Yokohama Math., J. 28(1980), 69–85.Google Scholar
[KK] Kishimoto, A. and Kumjian, A., Crossed products of Cuntz algebras by quasi-free automorphisms, In: Operator algebras and their applications, (eds. Fillmore, P. and Mingo, J.), Fields Institute Communications, to appear.Google Scholar
[OP] Olesen, D. and Pedersen, G.K., Some C* -dynamical systems with a single KMS state, Math., Scand. 42(1978), 111–118.Google Scholar
[Pa] Paschke, W., The crossed product of a C*-algebra by an endomorphism, Proc. Amer. Math., Soc. 80(1980), 113–118.Google Scholar
[Pd] Pedersen, G.K., C*-algebras and their automorphism groups, Academic Press, London, New York, San Francisco, 1979.Google Scholar
[Ph] Phillips, N.C., A classification theorem for nuclear purely infinite simple C*'-algebras, preprint.Google Scholar
[Re] Renault, J., A groupoid approach to C -algebras, Lecture Notes in Mathematics 793, Springer-Verlag, Berlin, Heidelberg, New York, 1980.Google Scholar
[RS] Rosenberg, J. and Schochet, C., The Kunneth theorem and the universal coefficient theorem for Kasparov s generalized K-functor, Duke Math., J. 55(1987), 431–474.Google Scholar
[Røl] Rørdam, M., Classification of certain infinite simple C*-algebras, J. Funct., Anal. 131(1995), 415–458.Google Scholar
[Rø2] Rørdam, M., Classification of certain infinite simpleC-algebras III, In: Operator algebras and their applications, (eds. Fillmore, P. and Mingo, J.), Fields Institute Communications, to appear.Google Scholar
[S] Schochet, C., Topological methods for C* -algebras II: geometric resolutions and the Kunneth formula, Pacific J., Math. 98(1982), 443–458.Google Scholar
[Ta] Takesaki, M., Duality for crossed products and the structure of von Neumann algebras of type III, Acta, Math. 131(1973), 249–310.Google Scholar
[Th] Thomsen, K., Inductive limits of interval algebras: the tracial state space, Amer. J., Math. 116(1994), 605–620.Google Scholar