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Cohomological Hall algebras and vertex algebras

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arxiv 2110.14356 v1 pith:AAURWUR5 submitted 2021-10-27 math.AG math.RT

Alexei Latyntsev This is my paper · ORCID
classification math.AGmath.RT
keywords hallalgebraalgebrascohomologicalvertexabelianapplicationbraided
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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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  1. Orthosymplectic modules of cohomological Hall algebras

    math.AG 2025-01 conditional novelty 7.0 of 10

    Classical type parabolic induction produces twisted Yetter-Drinfeld vertex modules for cohomological Hall algebras, including cases of dimension-zero sheaves on surfaces.

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