Cohomological Hall algebras and vertex algebras

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.

84 pages

References in corpus (3)

• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Equivariant geometry and the cohomology of the moduli space of curves
• The universal six-functor formalism

Cited by in corpus (2)

• Enumerative invariants and wall-crossing formulae in abelian categories
• Koszul algebras and Donaldson-Thomas invariants