Corpus ID: 55804272

# Chiral Homology of elliptic curves and Zhu's algebra

@article{Ekeren2018ChiralHO,
title={Chiral Homology of elliptic curves and Zhu's algebra},
author={Jethro van Ekeren and Reimundo Heluani},
journal={arXiv: Quantum Algebra},
year={2018}
}
• Published 30 March 2018
• Mathematics
• arXiv: Quantum Algebra
We study the chiral homology of elliptic curves with coefficients in a conformal 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.
8 Citations
Cosets of free field algebras via arc spaces
Using the invariant theory of arc spaces, we find minimal strong generating sets for certain cosets C of affine vertex algebras inside free field algebras that are related to classical Howe duality.Expand
On the nilpotent orbits arising from admissible affine vertex algebras
• Mathematics
• 2020
We give a simple description of the closure of the nilpotent orbits appearing as associated varieties of admissible affine vertex algebras in terms of primitive ideals.
Some remarks on associated varieties of vertex operator superalgebras
• H. Li
• Mathematics, Physics
• European Journal of Mathematics
• 2021
We study several families of vertex operator superalgebras from a jet (super)scheme point of view. We provide new examples of vertex algebras which are "chiralizations" of their Zhu's PoissonExpand
Singular Support of a Vertex Algebra and the Arc Space of Its Associated Scheme
• Mathematics
• Representations and Nilpotent Orbits of Lie Algebraic Systems
• 2019
Attached to a vertex algebra $${\mathcal V}$$ are two geometric objects. The associated scheme of $${\mathcal V}$$ is the spectrum of Zhu’s Poisson algebra $$R_{{\mathcal V}}$$. The singular supportExpand
Further 𝑞-series identities and conjectures relating false theta functions and characters
• Mathematics
• 2020
In this short note, a companion of [20], we discuss several families of $q$-series identities in connection to false and mock theta functions, characters of modules of vertex algebras, and "sum ofExpand
Jet schemes, Quantum dilogarithm and Feigin-Stoyanovsky's principal subspaces
• Mathematics
• 2020
We analyze the structure of the infinite jet algebra, or arc algebra, associated to level one Feigin-Stoyanovsky's principal subspaces. For $A$-series, we show that their Hilbert series can beExpand
A question of Joseph Ritt from the point of view of vertex algebras
• Mathematics
• 2020
Let $k$ be a field of characteristic zero. This paper studies a problem proposed by Joseph F. Ritt in 1950. Precisely, we prove that (1) If $p\geq 2$ is an integer, for every integerExpand
The singular support of the Ising model
• Mathematics
• 2020
We prove a new Fermionic quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson-Slater $q$-series identity of Rogers-Ramanujan type and to Nahm sumsExpand

#### References

SHOWING 1-10 OF 52 REFERENCES
Two-Dimensional Conformal Geometry and Vertex Operator Algebras
The focus of this volume is to formulate and prove one main theorem, the equivalance between the algebraic and geometric formulations of the notion of vertex operator algebra. The author introduces aExpand
Arc Spaces and Chiral Symplectic Cores
• Mathematics
• Publications of the Research Institute for Mathematical Sciences
• 2021
We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show that anyExpand
Abelianizing Vertex Algebras
To every vertex algebra V we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space gr(V) is naturally a vertex Poisson algebra, in particular aExpand
Arc spaces and the Rogers–Ramanujan identities
• Mathematics
• 2011
Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations, we obtain a newExpand
A short construction of the Zhu algebra
• Mathematics
• Journal of Algebra
• 2019
Abstract We investigate associative quotients of vertex algebras. We also give a short construction of the Zhu algebra, and a proof of its associativity using elliptic functions.
Quasi-lisse Vertex Algebras and Modular Linear Differential Equations
• Mathematics, Physics
• 2018
We introduce the notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertexExpand
Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries
• Mathematics
• 1989
Publisher Summary This chapter focuses on the conformal field theory (CFT) on universal family of stable curves with gauge symmetries. CFT has not only useful application to string theory andExpand
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities
• Mathematics, Physics
• 1993
We prove that the dimensions of coinvariants of certain nilpotent subalgebras of the Virasoro algebra do not change under deformation in the case of irreducible representations of (2,2r+1) minimalExpand
Configuration spaces of algebraic varieties
Abstract this paper Determines the rational cohomology ring of the configuration space of n -tuples of distinct points in a smooth complex projective variety X . The answer depends only on theExpand
Vertex Algebras and Algebraic Curves
Introduction Definition of vertex algebras Vertex algebras associated to Lie algebras Associativity and operator product expansion Applications of the operator product expansion Modules over vertexExpand