Representations of certain compact semigroups by semigroups
Authors:
J. H. Carruth and C. E. Clark
Journal:
Trans. Amer. Math. Soc. 149 (1970), 327337
MSC:
Primary 22.05
MathSciNet review:
0263964
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Abstract: An HLsemigroup 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 HLsemigroups to separate points of S; or equivalently, is S isomorphic to a strict projective limit of HLsemigroups? 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 HLsemigroups to separate points of S.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197002639640
PII:
S 00029947(1970)02639640
Keywords:
Compact semigroup,
Lie group,
Schützenberger group,
Hclass,
representation,
irreducible semigroup,
projective limit
Article copyright:
© Copyright 1970
American Mathematical Society
