Representations of certain compact semigroups by 𝐻𝐿-semigroups

Carruth, J. H.; Clark, C. E.

doi:10.1090/S0002-9947-1970-0263964-0

Representations of certain compact semigroups by $\textrm {HL}$-semigroups
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by J. H. Carruth and C. E. Clark PDF

Trans. Amer. Math. Soc. 149 (1970), 327-337 Request permission

Abstract:

An HL-semigroup is defined to be a topological semigroup with the property that the Schützenberger group of each $\mathcal {H}$-class is a Lie group. The following problem is considered: Does a compact semigroup admit enough homomorphisms into HL-semigroups to separate points of S; or equivalently, is S isomorphic to a strict projective limit of HL-semigroups? An affirmative answer is given in the case that S is an irreducible semigroup. If S is irreducible and separable, it is shown that S admits enough homomorphisms into finite dimensional HL-semigroups to separate points of S.

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