Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1681–1695 | Cite as

On the Center of a Hypergroupoid

  • Mahmood PourgholamhosseinEmail author
  • Mahmoud Kazemi Hokmabad
Original Paper


In this paper, we define the center of a hypergroupoid and investigate its properties. We also define isomorphism action on groupoids and show that for some particular groupoid \(\mathbb {G} \), the center of hypergroupoid \(\mathbb {G}^\mathbb {G}\) consists of all \( x^\mathbb {G} \), where x is in the center of \(\mathbb {G}\).


Hypergroupoid Center of groupoid Center of hypergroupoid Action on groupoid Isomorphism action 

Mathematics Subject Classification

22A22 20L05 20LXX 43A62 



We would like to thank Dr. Seyyed Mohammad Tabatabaie and the referee(s) for their valuable comments and suggestions, which helped us to considerably improve the manuscript.


  1. 1.
    Paterson, A.L.T.: Groupoids, Inverse Semigroups, and their Operator Algebras. Birkhauser, New York (1999)CrossRefGoogle Scholar
  2. 2.
    Renault, J.: A Groupoid Approach to \(C^*\)-algebras. Lecture Notes in Mathematics, vol. 793. Springer, Berlin (1980)Google Scholar
  3. 3.
    Jewett, R.I.: Spaces with an abstract convolution of measures. Adv. Math. 18, 1–101 (1975)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bloom, W.R., Heyer, H.: Harmonic Analysis of Probability Measures on Hypergroups. De Gruyter, Berlin (1995)CrossRefGoogle Scholar
  5. 5.
    Renault, J.: Induced representations and hypergroupoids. Symmetry, integrability and geometry: methods and applications SIGMA. 10 (2014)Google Scholar
  6. 6.
    Ross, K.A.: Centers of hypergroups. Trans. Am. Math. Soc. 243, 251–269 (1978)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ross, K.A.: Hypergroups and centers of measure algebras. In: 1st. Naz. Alta Mat. Symposia Mathematica, vol. XXII, pp. 189–203 (1977)Google Scholar
  8. 8.
    Tabatabaie, S.M., Pourgholamhossein, M., Amini, M., Kazemi Hokmabad, M.: Locally compact hypergroupoids. Indian J. Pure Appl. Math. (2018) (Accepted) Google Scholar

Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  • Mahmood Pourgholamhossein
    • 1
    Email author
  • Mahmoud Kazemi Hokmabad
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of QomQomIran
  2. 2.Department of MathematicsUniversity of QomQomIran

Personalised recommendations