Representations of certain compact semigroups by -semigroups

Authors:
J. H. Carruth and C. E. Clark

Journal:
Trans. Amer. Math. Soc. **149** (1970), 327-337

MSC:
Primary 22.05

DOI:
https://doi.org/10.1090/S0002-9947-1970-0263964-0

MathSciNet review:
0263964

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Abstract: An *HL*-semigroup is defined to be a topological semigroup with the property that the Schützenberger group of each -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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0263964-0

Keywords:
Compact semigroup,
Lie group,
Schützenberger group,
*H*-class,
representation,
irreducible semigroup,
projective limit

Article copyright:
© Copyright 1970
American Mathematical Society