• Corpus ID: 250264569

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

  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},
. 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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