Semi-Stable Chow-Hall Algebras of Quivers and Quantized Donaldson-Thomas Invariants

TL;DR

This paper introduces semi-stable Chow-Hall algebras for quivers, establishing their structural properties and linking quantized Donaldson-Thomas invariants to Chow-Betti numbers for symmetric quivers.

Contribution

It defines semi-stable Chow-Hall algebras, proves key structural results, and connects Donaldson-Thomas invariants with Chow-Betti numbers in symmetric cases.

Findings

Isomorphism of the cycle map

Tensor product decomposition of the algebra

Identification of invariants with Chow-Betti numbers

Abstract

The semi-stable 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 semi-stable loci in representation varieties of quivers. We prove several structural results on the semi-stable 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.