View article

Unfortunately, in [2] we overlooked a fundamental class of examples studied by Michael Voit ([3], Sections 5 and 6), which are also generalizations of the class of Dunkl-Ramirez discrete hypergroups [1], and their duals are also almost discrete, ie, one-point compactifications of discrete countably infinite spaces. These examples are clearly (hermitian) hypergroup deformations of the semigroup (Z+,<, max). Voit studied his class of examples to illustrate factorization of probability measures on certain symmetric, ie, hermitian hypergroups. In [2], we arrived at the class via necessary conditions for a hypergroup deformation (S,∗) of an infinite “max” semigroup (S,<,·) with identity, the first necessary condition being that (S,<,·) is isomorphic to (Z+,<, max). The sufficiency had a simple computational proof. Of course, it should have been attributed to Voit [3], had we been aware of this class of examples. As is clear from our …