  Consider the Cohomological Hall Algebra as defined by Kontsevich and
Soibelman, associated with a Dynkin quiver. We reinterpret the geometry behind
the multiplication map in the COHA, and give an iterated residue formula for
it. We show natural subalgebras whose product is the whole COHA (except in the
$E_8$ case). The dimension count version of this statement is an identity for
quantum dilogarithm series, first proved by Reineke. We also show that natural
structure constants of the COHA are universal polynomials representing
degeneracy loci, a.k.a. quiver polynomials.
