  Is every product system of Hilbert spaces over a semigroup $P$ concrete, i.e.
isomorphic to the product system of an $E_0$-semigroup over $P$? The answer, in
general, is no. We record a non-example when $P$ is cancellative and is not
embeddable in a group. However, we show that the answer is yes for a reasonable
class of semigroups which includes solid, Borel subsemigroups of locally
compact abelian groups.
