Some operator algebras from semigroups

Abstract

This is a study of reflexivity and structure properties of operator algebras generated by representations of the Heisenberg semigroup.We briefly revise earlier joint work with S.C. Power [14] on the continuous Heisenberg semigroup. We then show that the (restricted) left regular representation of the discrete Heisenberg semigroup gives rise to a reflexive operator algebra, which is semisimple. An example of a representation giving rise to a nonreflexive algebra is presented. Report on joint work with M. Anoussis (Aegean) and I.G. Todorov (Belfast) [2].