Character semigroups of locally compact inverse semigroups

Author:
Ronald O. Fulp

Journal:
Proc. Amer. Math. Soc. **27** (1971), 613-618

MSC:
Primary 22.05

MathSciNet review:
0276401

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Abstract: We show that if is a locally compact abelian continuous-inverse semigroup whose idempotent semigroup satisfies a certain technical condition on its prime ideals, then the maximal subgroups of the character semigroup of are obtained as inverse limits of the duals of the maximal subgroups of . It is shown that the technical conditions on are satisfied in each of the following cases: is compact, is totally disconnected, or is a chain. We then obtain necessary and sufficient conditions in order that a given inverse system of compact groups indexed by a totally disconnected semilattice admit a compatible compact semigroup topology on their disjoint union.

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DOI:
https://doi.org/10.1090/S0002-9939-1971-0276401-3

Keywords:
Locally compact abelian semigroups,
character semigroups,
inverse limits,
duals of maximal groups,
compact topologies,
totally disconnected semilattices

Article copyright:
© Copyright 1971
American Mathematical Society