Skip to main content

Remarks on the Pimsner-Voiculescu Embedding

  • Conference paper
  • First Online:
Operator Algebra and Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 58))

  • 1025 Accesses

Abstract

Irrational extended rotation algebras are shown to be C*-alloys in the sense of Exel (C R Math Acad Sci Soc R Can (2012), arXiv:1204.0486).

Mathematics Subject Classification (2010): 46L05, 46L55.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Effros, E.G., Shen, C.L.: The geometry of finite rank dimension groups. Illinois J. Math. 25(1), 27–38 (1981). URL http://projecteuclid.org/getRecord?id=euclid.ijm/1256047361

    Google Scholar 

  2. Elliott, G.A.: On the classification of inductive limits of sequences of semisimple finite-dimensional algebras. J. Algebra 38(1), 29–44 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  3. Elliott, G.A.: A property of totally ordered abelian groups. C. R. Math. Rep. Acad. Sci. Canada 1(2), 63–66 (1978/79)

    Google Scholar 

  4. Elliott, G.A.: On totally ordered groups, and K 0. In: Ring theory (Proc. Conf., Univ. Waterloo, Waterloo, 1978), Lecture Notes in Math., vol. 734, pp. 1–49. Springer, Berlin (1979)

    Google Scholar 

  5. Elliott, G.A.: On the classification of C -algebras of real rank zero. J. Reine Angew. Math. 443, 179–219 (1993). DOI 10.1515/crll.1993.443.179. URL http://dx.doi.org/10.1515/crll.1993.443.179

  6. Elliott, G.A.: A classification of certain simple C -algebras. II. J. Ramanujan Math. Soc. 12(1), 97–134 (1997)

    MATH  Google Scholar 

  7. Elliott, G.A., Evans, D.E.: The structure of the irrational rotation C -algebra. Ann. of Math. (2) 138(3), 477–501 (1993). DOI 10.2307/2946553. URL http://dx.doi.org/10.2307/2946553

    Google Scholar 

  8. Elliott, G.A., Loring, T.A.: AF embeddings of C(T 2) with a prescribed K-theory. J. Funct. Anal. 103(1), 1–25 (1992). DOI 10.1016/0022-1236(92)90130-B. URL http://dx.doi.org/10.1016/0022-1236(92)90130-B

  9. Elliott, G.A., Niu, Z.: The extended rotation algebra: Adjoining spectral projections to rotation algebras. J. Reine Angew. Math. 665, 1–71 (2012). DOI 10.1515/CRELLE.2011.112

    Article  MathSciNet  MATH  Google Scholar 

  10. Exel, R.: Blends and alloys. C. R. Math. Acad. Sci. Soc. R. Can. 35(3), 77–114 (2013)

    Google Scholar 

  11. Exel, R., Loring, T.A.: Invariants of almost commuting unitaries. J. Funct. Anal. 95(2), 364–376 (1991). DOI 10.1016/0022-1236(91)90034-3. URL http://dx.doi.org/10.1016/0022-1236(91)90034-3

    Google Scholar 

  12. Lin, H.: Homomorphisms from AH-algebras (2012), arXiv:1202.4631

    Google Scholar 

  13. Loring, T.A.: K-theory and asymptotically commuting matrices. Canad. J. Math. 40(1),197–216 (1988). DOI 10.4153/CJM-1988-008-9. URL http://dx.doi.org/10.4153/CJM-1988-008-9

    Google Scholar 

  14. Loring, T.A.: Berg’s technique for pseudo-actions with applications to AF embeddings. Canad. J. Math. 43(1), 119–157 (1991). DOI 10.4153/CJM-1991-008-5. URL http://dx.doi.org/10.4153/CJM-1991-008-5

    Google Scholar 

  15. Pimsner, M., Voiculescu, D.: Exact sequences for K-groups and Ext-groups of certain cross-product C -algebras. J. Operator Theory 4(1), 93–118 (1980)

    MathSciNet  MATH  Google Scholar 

  16. Pimsner, M., Voiculescu, D.: Imbedding the irrational rotation C -algebra into an AF-algebra. J. Operator Theory 4(2), 201–210 (1980)

    MathSciNet  MATH  Google Scholar 

  17. Pimsner, M.V.: Embedding some transformation group C -algebras into AF-algebras. Ergodic Theory Dynam. Systems 3(4), 613–626 (1983). DOI 10.1017/S0143385700002182. URL http://dx.doi.org/10.1017/S0143385700002182

    Google Scholar 

  18. Rieffel, M.A.: C -algebras associated with irrational rotations. Pacific J. Math. 93(2), 415–429 (1981). URL http://projecteuclid.org/getRecord?id=euclid.pjm/1102736269

    Google Scholar 

  19. Voiculescu, D.: Asymptotically commuting finite rank unitary operators without commuting approximants. Acta Sci. Math. (Szeged) 45(1–4), 429–431 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George A. Elliott .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Elliott, G.A., Niu, Z. (2013). Remarks on the Pimsner-Voiculescu Embedding. In: Carlsen, T., Eilers, S., Restorff, G., Silvestrov, S. (eds) Operator Algebra and Dynamics. Springer Proceedings in Mathematics & Statistics, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39459-1_6

Download citation

Publish with us

Policies and ethics