20
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

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

      Preprint

      , , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We study algebraic and topological properties of the convolution semigroups 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 \(G\)).

          Related collections

          Most cited references 5

          • Record: found
          • Abstract: not found
          • Article: not found

          Universal Objects in Some Classes of Clifford Topological Inverse Semigroups

           Olena Hryniv (2007)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Functors of probability measures in topological categories

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Idempotent measures on semigroups

               John S. Pym (1962)
                Bookmark

                Author and article information

                Journal
                06 November 2008
                2011-08-02
                Article
                10.1007/s00233-011-9319-5
                0811.1026

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                20M18, 20M30, 22A15, 43A05, 54B20, 54B30
                Semigroup Forum 83:1 (2011), 123-133
                math.GR math.GN

                Comments

                Comment on this article