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Hypergroup deformations of semigroups

  • Vishvesh KumarEmail author
  • Kenneth A. Ross
  • Ajit Iqbal Singh
Research Article
  • 14 Downloads

Abstract

We view the well-known example of the dual of a countable compact hypergroup, motivated by the orbit space of p-adic integers by Dunkl and Ramirez (Trans Am Math Soc 202:339–356, 1975), as hypergroup deformation of the max semigroup structure on the linearly ordered set \(\mathbb {Z}_+\) of the non-negative integers along the diagonal. This works as motivation for us to study hypergroups or semi convolution spaces arising from “max” semigroups or general commutative semigroups via hypergroup deformation on idempotents.

Keywords

Semigroups “Max” semigroups Discrete hypergroups Discrete semi-hypergroup Dunkl–Ramirez example Hypergroup deformation of idempotents Dual hypergroups 

Notes

Acknowledgements

The authors thank the referee for his/her kind comments and suggestions.

Vishvesh Kumar thanks the Council of Scientific and Industrial Research, India, for its senior research fellowship. He thanks his supervisors Ritumoni Sarma and N. Shravan Kumar for their support and encouragement. A preliminary version of a part of this paper was included in the invited talk by Ajit Iqbal Singh at the conference “The Stone-\(\check{\text{ C }}\)ech compactification: Theory and Applications, at Centre for Mathematical Sciences, University of Cambridge, July 6–8 2016” in honour of Neil Hindman and Dona Strauss. She is grateful to the organizers H.G. Dales and Imre Leader for the kind invitation, hospitality and travel support. She thanks them, Dona Strauss and Neil Hindman and other participants for useful discussion. She expresses her thanks to the Indian National Science Academy for the position of INSA Emeritus Scientist and travel support.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Vishvesh Kumar
    • 1
    Email author
  • Kenneth A. Ross
    • 2
  • Ajit Iqbal Singh
    • 3
  1. 1.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA
  3. 3.INSA Emeritus ScientistThe Indian National Science AcademyNew DelhiIndia

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