• Corpus ID: 250264569

# 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}
}
• Published 1 July 2022
• Mathematics
. 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…

## 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

### 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

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

### 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

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