• Corpus ID: 254685542

# BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks

@inproceedings{Davison2022BPSLA,
title={BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks},
author={Ben Davison and Lucien Hennecart and Sebastian Schlegel Mejia},
year={2022}
}
• Published 15 December 2022
• Mathematics
We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric Abelian categories $\mathcal{A}$ of homological dimension at most two, and a sheaf-theoretic BPS algebra under the conditions that $\mathcal{A}$ is 2-Calabi-Yau and has a good moduli space. We show that the BPS algebra for the preprojective algebra $\Pi_Q$ of a totally negative quiver is the free algebra generated by the intersection cohomology of the closure of the locus parameterising simple $\Pi_Q… 5 Citations • Mathematics • 2021 The aim of this paper is two-fold: Firstly, we prove Toda's$\chi\$-independence conjecture for Gopakumar--Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we introduce
We prove that the zero-ﬁber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this ﬁber, which were
• Ben DavisonLucien HennecartSebastian Schlegel Mejia
• Mathematics
• 2023
We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories whose stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of
We compare and generalize the different geometric constructions of the unipotent generalized Kac-Moody algebra associated to an arbitrary quiver. They happen to be connected to each other by