For any acyclic quiver partitioned into Dynkin subquivers, the cohomological Hall algebra is a tensor product of the subquiver Hall algebras, and Dynkin quiver polynomials multiply to classes of quiver strata.
Allman, Grothendieck classes of quiver cycles as iterated residues, Michigan Math
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A family of structure isomorphisms for the Cohomological Hall Algebra of an acyclic quiver
For any acyclic quiver partitioned into Dynkin subquivers, the cohomological Hall algebra is a tensor product of the subquiver Hall algebras, and Dynkin quiver polynomials multiply to classes of quiver strata.