Abstract
We give examples of ramification graphs having combinatorial origin. These graphs determine the group of dimensions and traces of the corresponding AF-algebras.
Similar content being viewed by others
Literature cited
A. M. Vershik, “Symmetric groups of high degree,” Dokl. Akad. Nauk SSSR,206, No. 2 (1972).
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).
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).
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.
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.
J. F. C. Kingman, “The representation of partition structures,” J. London Math. Soc.,18, 374–380 (1978).
J. F. C. Kingman, “Random partitions in population genetics,” Proc. R. Soc. London,A361, 1–20 (1978).
I. MacDonald, Symmetric Functions and Hall Polynomials [Russian trnaslation], Moscow (1985).
H. Poincaré, C. R. Acad. Sci. France,97, 1418 (1883).
L. Geissinger, “Hopf algebras of symmetric functions and class functions,” Lect. Notes Math.,579, 168–181 (1977).
G. James, Theory of Representations of Symmetric Groups [Russian translation], Moscow (1982).
G. Andrews, Theory of Partitions [Russian translation], Moscow (1982).
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
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
Issue Date:
DOI: https://doi.org/10.1007/BF01480687