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On the Group C*-Algebras of a Semidirect Product of Commutative and Finite Groups

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Abstract

Using representations of general position and their properties, we give a description of the group C*-algebras for semidirect products ℤd ⋊ G f , where G f is a finite group, in terms of algebras of continuous matrix functions defined on some compact set with boundary conditions. We give examples of the group C*-algebras of affine Coxeter groups.

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REFERENCES

  1. Yu. M. Berezans'kyi, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

    Google Scholar 

  2. V. Ostrovskyi and Yu. Samoilenko, Introduction to the Theory of Representations of Finitely Presented *-Algebras. I. Representations by Bounded Operators, Gordon and Breach, London (1999).

    Google Scholar 

  3. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge (1990).

    MATH  Google Scholar 

  4. N. Bourbaki, Groupes et Algebres de Lie IV–VI, Hermann, Paris (1968).

    Google Scholar 

  5. A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  6. G. W. Mackey, “Induced representations of locally compact groups,” Ann. Math., 55, No.1, 101–139 (1952).

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Dixmier, Les C*-Algebres et Leur Representations, Gauthier-Villars, Paris (1969).

    Google Scholar 

  8. J. M. G. Fell, “The structure of algebras of operator fields,” Acta Math., 106, No.3–4 (1961).

    Google Scholar 

  9. L. C. Grove and C. T. Benson, “Finite reflection groups,” Grad. Texts Math., 57, 173–185 (1977).

    Google Scholar 

  10. E. Jushenko, “On decomposition of affine Coxeter groups in semi-direct products,” J. Algebra Discr. Math., No. 3, 59–69 (2004).

    Google Scholar 

  11. A. Ya. Khelemskii, Banach and Polynormed Algebras: General Theory of Representations of Homology [in Russian], Nauka, Moscow (1989).

    Google Scholar 

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Authors and Affiliations

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

    Yu. S. Samoilenko

  2. Shevchenko Kyiv National University, Kyiv, Ukraine

    K. Yu. Yushchenko

Authors
  1. Yu. S. Samoilenko
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  2. K. Yu. Yushchenko
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 697–705, May, 2005.

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Samoilenko, Y.S., Yushchenko, K.Y. On the Group C*-Algebras of a Semidirect Product of Commutative and Finite Groups. Ukr Math J 57, 826–836 (2005). https://doi.org/10.1007/s11253-005-0232-5

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  • DOI: https://doi.org/10.1007/s11253-005-0232-5

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