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 | References | Similar Articles | Additional Information
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