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On compactification lattices of subsemigroups of \(\text{SL}(2,\mathbb R)\). (English) Zbl 1062.22017
If \(S\) is a topological semigroup a continuous homomorphism \(\kappa: S\to S^\kappa\) into a compact semigroup \(S^\kappa\) is called a semigroup compactification if \(\kappa(S)\) is dense in \(S^\kappa\). Using a glueing construction and the theory of Lie semigroups the authors construct semigroup compactifications for submonoids of SL\((2,\mathbb R)\) with dense interior. In this way they obtain e.g. all injective semigroup compactifications of exponential subsemigroups of SL\((2,\mathbb R)\). Moreover, they provide very explicit information on the structure of the compact semigroups they obtain as compactifications. Finally they also give some structural results on the lattice of all semigroup compactifications of a given submonoid.
MSC:
22E15 General properties and structure of real Lie groups
54H15 Transformation groups and semigroups (topological aspects)
22A15 Structure of topological semigroups
22A25 Representations of general topological groups and semigroups
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