Cohomological Hall algebras and vertex algebras

2021/10/27 by Latyntsev, Alexei
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2110.14356

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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