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Chiral Homology of elliptic curves and the Zhu algebra

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arxiv 1804.00017 v4 pith:32OEJYPR submitted 2018-03-30 math.QA math.AG

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keywords algebrahomologychiralcurvesellipticresultassociatedcoefficients
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We study the chiral homology of elliptic curves with coefficients in a quasiconformal vertex algebra. Our main result expresses the nodal curve limit of the first chiral homology group in terms of the Hochschild homology of the Zhu algebra of V. A technical result of independent interest regarding the equivalence between the associated graded with respect to Li's filtration and the arc space of the C_2 algebra is presented.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules

    math.QA 2025-11 conditional novelty 6.0 of 10

    Admissible-level affine sl2 modules and rational Virasoro minimal-model modules have matching characters under the substitution (w,q) -> (q^{+/-1/2}, q^3).

  2. The first chiral homology group in higher genus

    math.FA 2026-07 conditional novelty 5.5 of 10

    The genus-1 finiteness hypotheses of van Ekeren–Heluani imply finite-dimensional (and often vanishing) first chiral homology of a vertex algebra on every compact Riemann surface.

  3. On coefficients of operator product expansions for quantum field theories with ordinary, holomorphic, and topological spacetime dimensions

    hep-th 2025-02 conditional novelty 5.0 of 10

    For theories with mixed topological, holomorphic, and ordinary spacetime dimensions, OPE coefficients are proposed to be sheaf cohomology classes, with singular derived coefficients appearing under explicit dimension-...

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