BPS Lie algebras, perverse filtrations and shuffle algebras

TL;DR

This paper explicitly describes the BPS Lie algebra for quivers with zero potential and explores the perverse filtration in cohomological Hall algebras, proposing conjectures for more general cases.

Contribution

It provides an explicit description of the BPS Lie algebra for quivers with zero potential and relates perverse filtrations to polynomial limits, advancing understanding of these algebraic structures.

Findings

Explicit description of BPS Lie algebra for zero potential quivers

Relation between perverse filtration and polynomial limits

Partial description and conjecture for arbitrary potential cases

Abstract

We give an explicit description of the BPS Lie algebra of any quiver with zero potential, by relating the perverse filtration on the cohomological Hall algebra with certain limit conditions on polynomials. Our results also give a partial description of the perverse filtration for arbitrary potential, which we conjecture is complete in the case of tripled quivers with canonical cubic potential.