Cohomological Hall algebras and vertex algebras

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 set...

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Bibliographic Details
Published in:arXiv.org 2021-10
Main Author: Latyntsev, Alexei
Format: Article
Language:English
Subjects:
Algebra
Homology
Sheaves
Online Access:Get full text
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Summary: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.
ISSN:2331-8422