# A short construction of the Zhu algebra

@article{vanEkeren2019ASC,
title={A short construction of the Zhu algebra},
author={Jethro van Ekeren and Reimundo Heluani},
journal={Journal of Algebra},
year={2019}
}
• Published 30 March 2018
• Mathematics
• Journal of Algebra
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.
3 Citations
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#### References

SHOWING 1-10 OF 13 REFERENCES
Superconformal Vertex Algebras and Jacobi Forms
We discuss the appearance of Jacobi automorphic forms in the theory of superconformal vertex algebras, explaining it by way of supercurves and formal geometry. We touch on some related topics such asExpand
Vertex Operator Algebras and Associative Algebras
• Mathematics
• 1996
LetVbe a vertex operator algebra. We construct a sequence of associative algebrasAn(V) (n = 0, 1, 2,…) such thatAn(V) is a quotient ofAn + 1(V) and a pair of functors between the categoryExpand
Finite vs affine W-algebras
• Mathematics, Physics
• 2006
Abstract.In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the λ-bracket. In Section 2 weExpand
Modular invariance of characters of vertex operator algebras
In contrast with the finite dimensional case, one of the distinguished features in the theory of infinite dimensional Lie algebras is the modular invariance of the characters of certainExpand
$\phi$-coordinated modules for quantum vertex algebras and associative algebras
We study $\N$-graded $\phi$-coordinated modules for a general quantum vertex algebra $V$ of a certain type in terms of an associative algebra $\widetilde{A}(V)$ introduced by Y.-Z. Huang. Among theExpand
Differential equations, duality and modular invariance
We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the followingExpand
Vertex algebras for beginners
Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: CalculusExpand
ELLIPTIC FUNCTIONS
The first systematic account of the theory of elliptic functions and the state of the art around the turn of the century. Preceding general class field theory and therefore incomplete. Contains aExpand
Modular Functions and Dirichlet Series in Number Theory
This is the second volume of a 2-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volumeExpand
Vertex algebras for beginners, volume 10 of University Lecture Series
• American Mathematical Society, Providence, RI, second edition,
• 1998