Skip to main content
SpringerLink
Log in

Combinatorial examples in the theory of AF-algebras

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

We give examples of ramification graphs having combinatorial origin. These graphs determine the group of dimensions and traces of the corresponding AF-algebras.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. M. Vershik, “Symmetric groups of high degree,” Dokl. Akad. Nauk SSSR,206, No. 2 (1972).

  2. A. M. Vershik and S. V. Kerov, “Locally semisimple algebras. Combinatorial theory and K0-functor,” Itogi Nauki Tekhn., Ser. Sovrem. Probl. Matem., Nov. Dostizh.,26, 3–56 (1955).

    Google Scholar 

  3. A. M. Vershik and S. V. Kerov, “K-functor (Grothendieck group) of the infinite symmetric group,” in: Zapiski Nauchn. Semin. Leningr. Otdel. Mat. Inst.,123, 126–151 (1983).

    Google Scholar 

  4. S. V. Kerov and A. M. Vershik, “Characters, factor-representations and K-functor of the infinite symmetric group,” in: Proc. Int. Conf. Oper. Alg., Vol. 1 (1980), pp. 23–32.

    Google Scholar 

  5. S. V. Kerov, “Polynomial groups of dimensions,” in: Theory of Operators and Theory of Functions [in Russian], Vol. 1, LGU, Leningrad (1983), pp. 185–194.

    Google Scholar 

  6. J. F. C. Kingman, “The representation of partition structures,” J. London Math. Soc.,18, 374–380 (1978).

    Google Scholar 

  7. J. F. C. Kingman, “Random partitions in population genetics,” Proc. R. Soc. London,A361, 1–20 (1978).

    Google Scholar 

  8. I. MacDonald, Symmetric Functions and Hall Polynomials [Russian trnaslation], Moscow (1985).

  9. H. Poincaré, C. R. Acad. Sci. France,97, 1418 (1883).

    Google Scholar 

  10. L. Geissinger, “Hopf algebras of symmetric functions and class functions,” Lect. Notes Math.,579, 168–181 (1977).

    Google Scholar 

  11. G. James, Theory of Representations of Symmetric Groups [Russian translation], Moscow (1982).

  12. G. Andrews, Theory of Partitions [Russian translation], Moscow (1982).

Download references

Authors
  1. S. V. Kerov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 55–67, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kerov, S.V. Combinatorial examples in the theory of AF-algebras. J Math Sci 59, 1063–1071 (1992). https://doi.org/10.1007/BF01480687

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01480687

Search

Navigation