2019/08/01 by Justin Allman, Allman, Justin
Mathematics · #57R20 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 16G20 #Representation Theory (math.RT) #Secondary 55R40
paper · pdf · doi:10.48550/arxiv.1908.00567
openalex publication_date 2019/08/01 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28
For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The family is parameterized by partitions of the quiver into Dynkin subquivers. For each such partition, we write the domain of our isomorphism as a tensor product of subalgebras in two ways. In the first, each tensor factor is isomorphic to the CoHA of the quiver with a single vertex and no arrows. In the second, the tensor factors are each isomorphic to the CoHAs of the corresponding Dynkin subquivers. When the quiver is already an orientation of a simply-laced Dynkin diagram, our results interpolate between isomorphisms proved by Rimanyi. Such CoHA decompositions appear in prior work of Davison--Meinhardt and Franzen--Reineke, but our proof gives an explicit topological realization of these results. As a consequence of our method, we deduce that certain structure constants in the CoHA naturally arise as CoHA products of classes of Dynkin quiver polynomials.