# 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} }

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

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