On cohomological Hall algebras of quivers : Yangians

TL;DR

This paper explores the structure of cohomological Hall algebras associated with quivers, conjectures their equivalence to Yangians, and constructs an embedding linking the two algebraic structures through their actions on quiver variety cohomology.

Contribution

It introduces a conjecture relating cohomological Hall algebras to Yangians and constructs an explicit embedding between them, advancing understanding of their algebraic relationship.

Findings

Conjecture that Y equals the Yangian after scalar extension.

Constructed an embedding of Y into the Yangian.

Intertwines actions of both algebras on quiver variety cohomology.

Abstract

We consider the cohomological Hall algebra Y of a Lagrangian substack of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and its actions on the cohomology of quiver varieties. We conjecture that Y is equal, after a suitable extension of scalars, to the Yangian introduced by Maulik and Okounkov, and we construct an embedding of Y in the Yangian, intertwining the respective actions of both algebras on the cohomology of quiver varieties.