On the Semi-Stable CoHa and its Modules Arising from Smooth Models

TL;DR

This paper introduces the semi-stable ChowHa, a new algebraic structure derived from equivariant Chow groups, and demonstrates that smooth models of quiver moduli produce cyclic modules over it, with explicit presentations.

Contribution

It constructs the semi-stable ChowHa as a quotient of the CoHa and analyzes modules from smooth quiver moduli using Harder-Narasimhan techniques.

Findings

The semi-stable ChowHa is a quotient of the CoHa.

Modules from smooth quiver models are cyclic.

Explicit presentations of these modules are obtained.

Abstract

We study a variant of the semi-stable Cohomological Hall algebra which we construct using equivariant Chow groups. This algebra, we call it the semi-stable ChowHa, arises as a quotient of the CoHa. Smooth models of quiver moduli give rise to modules over the semi-stable ChowHa. We prove that these modules are cyclic and we compute a presentation using Harder-Narasimhan methods.