  Starting with a very pedestrian point of view we compare two different at the
first glance definitions for an algebra associated to BPS states in
supersymmetric fields theories. One proposed by Harvey and Moore exploits
$S$-matrices of BPS states as structure constants of a new algebra. Another one
proposed by Kontsevich and Soibelman gives a construction according to the
structure of cohomological Hall algebras. We show these two constructions give
equivalent algebras.
