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Consider the Cohomological Hall Algebra as defined by Kontsevich andSoibelman, associated with a Dynkin quiver. We reinterpret the geometry behindthe multiplication map in the COHA, and give an iterated residue formula forit. 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 forquantum dilogarithm series, first proved by Reineke. We also show that naturalstructure constants of the COHA are universal polynomials representingdegeneracy loci, a.k.a. quiver polynomials.

On the Cohomological Hall Algebra of Dynkin quivers