Journal of Lie Theory Vol. 14, No. 1, pp. 73109 (2004) 

On Compactification Lattices of Subsemigroups of SL(2,R)Brigitte E. Breckner and Wolfgang A. F. RuppertB. E. BrecknerBabe\c sBolyai University Faculty of Mathematics and Computer Science Str. M. Kog\u alniceanu 1 RO3400 ClujNapoca Romania brigitte@math.ubbcluj.ro and W. A. F. Ruppert Institut für Mathematik und Angewandte Statistik Universität für Bodenkultur Peter Jordanstr. 82 A1190 Wien Austria ruppert@edv1.boku.ac.at Abstract: Using the tools introduced in [Breckner, B. E., and W. A. F. Ruppert, J. Lie Theory 11 (2001), 559604], we investigate topological semigroup compactifications of closed connected submonoids with dense interior of Sl(2,R). In particular, we show that the growth of such a compactification is always contained in the minimal ideal, and describe the subspace of all minimal idempotents (typically a twocell) and the maximal subgroups (these are always isomorphic with a compactification of R). For a large class of such semigroups we give explicit constructions yielding all possible topological semigroup compactifications and determine the structure of the compactification lattice. Keywords: Bohr compactification, lattice of compactifications, asymptotic homomorphism, subsemigroups of Sl(2,R), Lie semigroups, Lie semialgebras, diamond product, rectangular domain, umbrella set, divisible semigroup, UDC semigroup Classification (MSC2000): 22E15; 22E46, 22A15, 22A25 Full text of the article:
Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.
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