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[2108.10338] DT invariants from vertex algebras

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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 $\mathcal{H}_Q$ is naturally identified with the graded dual vector space of the principal free vertex algebra associated to the Euler form of $Q$; the product of $\mathcal{H}_Q$ arises from an isomorphism of the latter with the universal enveloping vertex algebra of a certain vertex Lie algebra. This leads to a new interpretation of Donaldson--Thomas invariants of $Q$ (and, in particular, re-proves their positivity), and to a new interpretation of CoHA modules made of cohomologies of non-commutative Hilbert schemes.

[2108.10338] DT invariants from vertex algebras --> Mathematics > Algebraic Geometry arXiv:2108.10338 (math) [Submitted on 23 Aug 2021 ( v1 ), last revised 30 Nov 2021 (this version, v2)] Title: DT invariants from vertex algebras Authors: Vladimir Dotsenko , Sergey Mozgovoy View a PDF of the paper titled DT invariants from vertex algebras, by Vladimir Dotsenko and Sergey Mozgovoy View PDF Abstract: 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 $\

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