Algebras and Representation Theory

, Volume 15, Issue 1, pp 29–51 | Cite as

Representation Theory of Polyadic Groups

Open Access
Article

Abstract

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

Keywords

Polyadic groups Representations Retract of n-ary groups Covering groups 

Mathematics Subject Classification (2010)

20N15 

References

  1. 1.
    Borowiec, A., Dudek, W.A., Duplij, S.: Bi-element representations of ternary groups. Commun. Algebra 34, 1651–1670 (2006)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Dörnte, W.: Unterschungen über einen verallgemeinerten Gruppenbegriff. Math. Z. 29, 1–19 (1929)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Dudek, W.A.: Remarks on n-groups. Demonstr. Math. 13, 165–181 (1980)MATHMathSciNetGoogle Scholar
  4. 4.
    Dudek, W.A.: On n-ary group with only one skew element. Rad. Mat. (Sarajevo) 6, 171–175 (1990)MATHMathSciNetGoogle Scholar
  5. 5.
    Dudek, W.A., Glazek, K.: Around the Hosszú–Gluskin Theorem for n-ary groups. Discrete Math. 308, 4861–4876 (2008)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Dudek, W.A., Glazek, K., Gleichgewicht, B.: A note on the axioms of n-groups. Colloq. Math. Soc. János Bolyai 29, 195–202 (1977)MathSciNetGoogle Scholar
  7. 7.
    Dudek, W.A., Michalski, J.: On a generalization of Hosszú theorem. Demonstr. Math. 15, 437–441 (1982)MathSciNetGoogle Scholar
  8. 8.
    Dudek, W.A., Michalski, J.: On retract of polyadic groups. Demonstr. Math. 17, 281–301 (1984)MATHMathSciNetGoogle Scholar
  9. 9.
    Głazek, K., Gleichgewicht, B.: Abelian n-groups. Colloq. Math. Soc. János Bolyai 29, 321–329 (1977)Google Scholar
  10. 10.
    Gleichgewicht, B., Wanke-Jakubowska, M.B., Wanke-Jerie, M.E.: On representations of cyclic n-groups. Demonstr. Math. 16, 357–365 (1983)MATHMathSciNetGoogle Scholar
  11. 11.
    Grzymala-Busse, J.W.: Automorphisms of polyadic automata. J. Assoc. Comput. Mach. 16, 208–219 (1969)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Kasner, E.: An extension of the group concept. Bull. Am. Math. Soc. 10, 290–291 (1904)Google Scholar
  13. 13.
    Kerner, R.: Ternary and non-associative algebraic structures and their applications in physics. Univ. P. and M. Curie, Paris (2000)Google Scholar
  14. 14.
    Michalski, J.: Covering k-groups of n-groups. Arch. Math. (Brno) 17, 207–226 (1981)MATHMathSciNetGoogle Scholar
  15. 15.
    Nikshych, D., Vainerman, L.: Finite quantum groupoids and their applications. Univ. California, Los Angeles (2000)Google Scholar
  16. 16.
    Pojidaev, A.P.: Enveloping algebras of Fillipov algebras. Commun. Algebra 31, 883–900 (2003)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Post, E.L.: Polyadic groups. Trans. Am. Math. Soc. 48, 208–350 (1940)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Vainerman, L., Kerner, R.: On special classes of n-algebras. J. Math. Phys. 37, 2553–2565 (1996)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Wanke-Jakubowska, M.B., Wanke-Jerie, M.E.: On representations of n-groups. Ann. Sci. Math. Polonae. Comment. Math. 24, 335–341 (1984)MATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland
  2. 2.Department of Pure Mathematics, Faculty of Mathematical SciencesUniversity of TabrizTabrizIran

Personalised recommendations