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Semigroup Forum

, 83:123 | Cite as

Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups

  • Taras Banakh
  • Matija Cencelj
  • Olena Hryniv
  • Dušan Repovš
RESEARCH ARTICLE

Abstract

We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup \(\exp(G)\) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G).

Keywords

Convolution semigroup Global semigroup Hypersemigroup Clifford semigroup Regular semigroup Topological group Radon measure Weakly normal monadic functor 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Taras Banakh
    • 1
    • 2
  • Matija Cencelj
    • 3
  • Olena Hryniv
    • 2
  • Dušan Repovš
    • 4
  1. 1.Instytut MatematykiJan Kochanowski UniversityKielcePoland
  2. 2.Department of MathematicsIvan Franko National University of LvivLvivUkraine
  3. 3.Institute of Mathematics, Physics and Mechanics, and Faculty of EducationUniversity of LjubljanaLjubljanaSlovenia
  4. 4.Faculty of Mathematics and Physics, and Faculty of EducationUniversity of LjubljanaLjubljanaSlovenia

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