  A higher rank numerical semigroup is a positive cone whose seminormalization
is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint
semigroup algebras are known to provide examples that answer Arveson's Dilation
Problem to the negative. Here we show that these algebras share the polydisc as
the character space in a canonical way. We subsequently use this feature in
order to identify higher rank numerical semigroups from the corresponding
nonselfadjoint algebras.
