A family of structure isomorphisms for the Cohomological Hall Algebra of an acyclic quiver.

For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The domain of each isomorphism is a tensor product of subalgebras in which each factor is isomorphic to the CoHA of the quiver with a single vertex and no arrows. Our result gives a topological interpretation for some CoHA decompositions in terms of stability conditions due to Franzen--Reineke and, in the case where the quiver is an orientation of a simply-laced Dynkin diagram, interpolates between isomorphisms proved by Rimanyi. As a consequence of our results, we see that every acyclic CoHA can be written as a tensor product of CoHAs corresponding to Dynkin subquivers, and furthermore, that certain structure constants in the CoHA naturally arise as CoHA products of classes of so-called Dynkin quiver polynomials.