Koszul algebras and Donaldson–Thomas invariants

Dotsenko, Vladimir; Feigin, Evgeny; Reineke, Markus

doi:10.1007/s11005-022-01604-4

Lett Math Phys

2022

DOI: 10.1007/s11005-022-01604-4

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Koszul algebras and Donaldson–Thomas invariants

Vladimir Dotsenko

Evgeny Feigin

Markus Reineke

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2024

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Dt Invariants From Vertex Algebras

Dotsenko,

Mozgovoy

2024

J. Inst. Math. Jussieu

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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 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.

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Dt Invariants From Vertex Algebras

Dotsenko,

Mozgovoy

2024

J. Inst. Math. Jussieu

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show abstract

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Koszul algebras and Donaldson–Thomas invariants

Cited by 1 publication

References 21 publications

Dt Invariants From Vertex Algebras

Dt Invariants From Vertex Algebras

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