Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

Abstract

The semistable ChowHa of a quiver with stability is defined as an analog of the cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups of semistable loci in representation varieties of quivers. We prove several structural results on the semistable ChowHa, namely isomorphism of the cycle map, a tensor product decomposition, and a tautological presentation. For symmetric quivers, this leads to an identification of their quantized Donaldson–Thomas invariants with the Chow–Betti numbers of moduli spaces.