2021 年 73 巻 1 号 p. 185-209
We introduce a simple, self-dual, rational, and 𝐶2-cofinite vertex operator algebra of CFT-type associated with a ℤ𝑘-code for 𝑘 ≥ 2. Our argument is based on the ℤ𝑘-symmetry among the simple current modules for the parafermion vertex operator algebra 𝐾(𝔰𝔩2, 𝑘). We show that it is naturally realized as the commutant of a certain subalgebra in a lattice vertex operator algebra. Furthermore, we construct all the irreducible modules inside a module for the lattice vertex operator algebra.
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