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On the *-representation of one class of algebras associated with Coxeter graphs

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Abstract

We investigate *-representations of a class of algebras that are quotient algebras of the Hecke algebras associated with Coxeter graphs. A description of all unitarily nonequivalent irreducible *-representations of finite-dimensional algebras is given. We prove that only trees that have at most one edge of type s > 3 define algebras of finite Hilbert type for all values of parameters.

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References

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

  2. N. D. Popova, Yu. S. Samoilenko, and O. V. Strilets’, “On the growth of deformations of algebras associated with Coxeter graphs,” Ukr. Mat. Zh., 59, No. 6, 826–837 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  3. N. Popova, “On one algebra of Temperley-Lieb type,” in: Proceedings of the Institute of Mathematics, Ukrainian National Academy of Sciences [in Ukrainian], Vol. 43, Part 2 (2002), pp. 486–489.

    MathSciNet  Google Scholar 

  4. M. A. Vlasenko and N. D. Popova, “On configurations of subspaces of a Hilbert space with fixed angles between them,” Ukr. Mat. Zh., 56, No. 5, 606–615 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  5. N. D. Popova and Yu. S. Samoilenko, “On the existence of configurations of subspaces in a Hilbert space with fixed angles” J. Symmetry, Integr. Geom.: Meth. Appl., 2, No. 55, 1–5 (2006).

    MathSciNet  Google Scholar 

  6. S. V. Ivanov and N. D. Popova, “On representation of some algebras associated with Coxeter graphs,” Uchen. Zap. Tavrich. Univ., Ser. Mat. Mekh. Inform. Kibern., 19(58), No. 1, 1–11 (2005).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    N. D. Popova, Yu. S. Samoilenko & O. V. Strilets’

Authors
  1. N. D. Popova
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  2. Yu. S. Samoilenko
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  3. O. V. Strilets’
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 545–556, April, 2008.

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Popova, N.D., Samoilenko, Y.S. & Strilets’, O.V. On the *-representation of one class of algebras associated with Coxeter graphs. Ukr Math J 60, 623–638 (2008). https://doi.org/10.1007/s11253-008-0072-1

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  • DOI: https://doi.org/10.1007/s11253-008-0072-1

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