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

Using the tools introduced in [2] 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 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.