On Compactification Lattices of Subsemigroups of SL(2, R)

摘要

Using the tools introduced in a previous article of the authors [ J. Lie Theory 11 (2001), 559--604] 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 two-cell) and the maximal subgroups (these are always isomorphic to 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.