  Idempotent states on locally compact quantum semigroups with weak
cancellation properties are shown to be Haar states on a certain sub-object
described by an operator system with comultiplication. We also give a
characterization of the situation when this sub-object is actually a compact
quantum subgroup. In particular we reproduce classical results on idempotent
probability measures on locally compact semigroups with cancellation.

Operator Algebras;Functional Analysis;Quantum Algebra