# On rationality of $\mathbb{C}$-graded vertex algebras and applications to Weyl vertex algebras under conformal flow

@inproceedings{Barron2022OnRO, title={On rationality of \$\mathbb\{C\}\$-graded vertex algebras and applications to Weyl vertex algebras under conformal flow}, author={Katrina Barron and Karina Batistelli and Florencia Orosz Hunziker and Veronika Pedic Tomic and Gaywalee Yamskulna}, year={2022} }

. Using the Zhu algebra for a certain category of C -graded vertex algebras V , we prove that if V is ﬁnitely Ω -generated and satisﬁes suitable grading conditions, then V is rational, i.e. has semi-simple representation theory, with one dimensional level zero Zhu algebra. Here Ω denotes the vectors in V that are annihilated by lowering the real part of the grading. We apply our result to the family of rank one Weyl vertex algebras with conformal element ω µ parameterized by µ ∈ C , and prove…

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## References

SHOWING 1-10 OF 42 REFERENCES

### {{C}}-Graded vertex algebras and conformal flow

- Mathematics
- 2014

We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by “lowest weight vectors.” We show that such vertex algebras have a…

### Vertex Operator Algebras Associated to Admissible Representations of

- Mathematics
- 1995

Abstract: The Kac-Wakimoto admissible modules for
$\hat{sl}_2$ are studied from the point of view of vertex operator algebras. It is shown that the vertex operator algebra L(l,0) associated to…

### On generators and relations for higher level Zhu algebras and applications

- Mathematics
- 2021

Abstract. We give some general results about the generators and relations for the higher level Zhu algebras for a vertex operator algebra. In particular, for any element u in a vertex operator…

### On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras

- MathematicsJournal of Algebra
- 2019

### Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and their Generalized Modules

- Mathematics
- 2014

This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory…

### Vertex Algebras and Algebraic Curves

- Mathematics
- 2000

Introduction Definition of vertex algebras Vertex algebras associated to Lie algebras Associativity and operator product expansion Applications of the operator product expansion Modules over vertex…

### Classification of irreducible modules of the vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of an arbitrary rank

- Mathematics
- 2008

### C_2-cofinite W-algebras and their logarithmic representations

- Mathematics
- 2012

We discussour recentresultsonthe representationtheoryofW-algebras relevant to Logarithmic Conformal Field Theory. First we explain some general constructions of W-algebras coming from screening…

### Modular invariance of characters of vertex operator algebras

- Mathematics
- 1995

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 certain…

### $C_2$-cofiniteness of the vertex algebra $V_L^+$ when $L$ is a non-degenerate even lattice

- Mathematics
- 2009

It was shown by Abe, Buhl and Dong that the vertex algebra $V_L^+$ and its irreducible weak modules satisfy the $C_2$-cofiniteness condition when $L$ is a positive definite even lattice. In this…