Equivariant Cohomological Hall Algebras and Yangians

Abstract: Given a quiver Q with potential W, Konstevich and Soibelman defined Cohomological Hall algebras(CoHA) which is certain associative algebra on the cohomology of moduli space of quiver representations. These algebras are way too big, and to study them Davison and Meinhardt, introduced BPS lie algebras which by a PBW-type theorem can be thought of as the building blocks of these algebras. By considering the extra action of torus, Schiffmann and Vasserot used the Equivariant version of these algebras in their proof of AGT conjectures. In this talk, I will define these algebras and explain how they relate to Yangians. In particular, I will try to explain recent work of Davison where by defining deformed and affinized version of BPS lie algebras, he shows that the fully Equivariant CoHA for the case of tripled loop quiver with canonical potential is same as the positive half of the Affine Yangian of gl(1).