On rationality of C-graded vertex algebras and applications to Weyl vertex algebras under conformal flow - INSPIRE

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On rationality of C-graded vertex algebras and applications to Weyl vertex algebras under conformal flow

Katrina Barron
(
- U. Notre Dame, Dept. Math.
)
,
Karina Batistelli
(
- U. Chile, Santiago
)
,
Florencia Orosz Hunziker
(
- Denver U.
)
,
Veronika Pedic Tomic
(
- Zagreb U.
)
,
Gaywalee Yamskulna
(
- Illinois State U.
)

Jul 1, 2022

Published in:

J.Math.Phys. 63 (2022) 9, 091706

Published: Sep 20, 2022

e-Print:

2207.00638 [math.RT]

DOI:

10.1063/5.0117895

View in:

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Abstract: (AIP)

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., it has semi-simple representation theory, with a 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 ωμ parameterized by μ∈C and prove that for certain non-integer values of μ, these vertex algebras, which are non-integer graded, are rational, with a one-dimensional level zero Zhu algebra. In addition, we generalize this result to appropriate C-graded Weyl vertex algebras of arbitrary ranks.

Note:

Final version. Typos corrected and bibliography updated. We thank the referee for their comments and suggestions. To appear in Journal of Mathematical Physics

algebra: vertex
dimension: 1
Weyl
conformal
category
graded
family
flow
Rational vertex algebras
Weyl vertex algebras

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