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arXiv · 2110.14356

Cohomological Hall algebras and vertex algebras

Alexei Latyntsev
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Abstract

The moduli stack of representations of a quiver, or coherent sheaves on a proper curve, carries two structures on its cohomology: a Hall algebra and braided vertex coalgebra. We show that they are compatible, by developing a formulation of abelian localisation which works in the derived/singular setting. An application of these techniques gives an explicit formula for the cohomological Hall algebra products.

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Alexei Latyntsev. 2021-10-27. Cohomological Hall algebras and vertex algebras. https://arxiv.org/abs/2110.14356

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