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Structure of the Systems of Orthogonal Projections Connected with Countable Coxeter Trees

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Ukrainian Mathematical Journal Aims and scope

The paper is devoted to the investigation of representations of Temperley–Lieb-type algebras generated by orthogonal projections connected with countable Coxeter trees. The theorem on the structure of these systems of orthogonal projections is proved. Some examples are presented.

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References

  1. H. N. V. Temperley and E. H. Lieb, “Relations between ‘percolations’ and ‘coloring’ problems and other graph theoretical problems associated with regular planar lattices: some exact results for the percolation problem,” Proc. Roy. Soc. London. A, 322, 251–280 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  2. Yu. S. Samoilenko and A.V. Strelets, “On simple n-tuples of subspaces in a Hilbert space,” Ukr. Mat. Zh., 61, No. 12, 1668–1703 (2009); English translation: Ukr. Math. J., 61, No. 12, 1956–1994 (2009).

  3. P. G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Springer, New York (2013).

    Book  Google Scholar 

  4. D. Cvetkovĭć, M. Doob, and H. Sachs, Spectra of Graphs. Theory and Applications, VEB Deutscher Verlag der Wissenschaften, Berlin (1980).

    Google Scholar 

  5. A. E. Brouwer and W. H. Haemers, Spectra of Graphs, Springer, New York (2012).

    Book  MATH  Google Scholar 

  6. F. M. Goodman, P. de la Harpe, and V. F. R. Jones, Coxeter Graphs and Towers of Algebras, Springer, New York (1989).

    Book  MATH  Google Scholar 

  7. Yu. S. Samoilenko and L. M. Tymoshkevych, “On the spectral theory of Coxeter graphs,” U Sviti Mat., 15, No. 3, 14–24 (2009).

    Google Scholar 

  8. B. Mohar and W. Woess, “A survey on spectra of infinite graphs,” Bull. London Math. Soc., 21, 209–234 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Mohar, “The spectrum of an infinite graph,” Linear Alg. Appl., 48, 245–256 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  10. J. von Below, “An index theory for uniformly locally finite graphs,” Linear Alg. Appl., 431, 1–19 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  11. A. S. Korotkov and L. M. Tymoshkevych, “An analog of the Smith theorem for countable Coxeter graphs,” Dop. Nats. Akad. Nauk Ukr., No. 12, 19–24 (2013).

  12. J. Graham, Modular Representations of Hecke Algebras and Related Algebras, Ph.D. Thesis, Sydney (1995).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 9, pp. 1185–1192, September, 2014.

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Kyrychenko, A.A., Samoilenko, Y.S. & Tymoshkevych, L.M. Structure of the Systems of Orthogonal Projections Connected with Countable Coxeter Trees. Ukr Math J 66, 1324–1332 (2015). https://doi.org/10.1007/s11253-015-1012-5

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  • DOI: https://doi.org/10.1007/s11253-015-1012-5

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