DT invariants from vertex algebras
| Autor: | Vladimir Dotsenko, Sergey Mozgovoy |
|---|---|
| Přispěvatelé: | Institut de Recherche Mathématique Avancée (IRMA), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), Trinity College Dublin, University of Strasbourg Institute for Advanced Study (USIAS) Fellowship USIAS-2021-061, Institut Universitaire de France, ANR-20-CE40-0016,HighAGT,Algèbre, Géométrie, et Topologie Supérieures(2020), Dotsenko, Vladimir, Algèbre, Géométrie, et Topologie Supérieures - - HighAGT2020 - ANR-20-CE40-0016 - AAPG2020 - VALID |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | HAL |
| Popis: | We obtain a new interpretation of the cohomological Hall algebra $\mathcal{H}_Q$ of a symmetric quiver $Q$ in the context of the theory of vertex algebras. Namely, we show that the graded dual of $\mathcal{H}_Q$ is naturally identified with the underlying vector space of the principal free vertex algebra associated to the Euler form of $Q$. Properties of that vertex algebra are shown to account for the key results about $\mathcal{H}_Q$. In particular, it has a natural structure of a vertex bialgebra, leading to a new interpretation of the product of $\mathcal{H}_Q$. Moreover, it is isomorphic to the universal enveloping vertex algebra of a certain vertex Lie algebra, which leads to a new interpretation of Donaldson--Thomas invariants of $Q$ (and, in particular, re-proves their positivity). Finally, it is possible to use that vertex algebra to give a new interpretation of CoHA modules made of cohomologies of non-commutative Hilbert schemes. Comment: 43 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|