On compactification lattices of subsemigroups of Sl(2,R), submitted to Journal of Lie Theory

Abstract. Using the tools introduced in [2] we investigate topological semigroup compactifications of closed connected submonoids with dense in-terior of Sl(2,R). In particular, we show that the growth of such a compact-ification 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