Abstract
We construct a vertex operator algebra associated with a \(\mathbf{Z}/k\mathbf{Z}\)-code of length n for an integer \(k \ge 2\). We realize it inside a lattice vertex operator algebra as the commutant of a certain subalgebra. The vertex operator algebra is isomorphic to a known one in the cases \(k = 2,3\).
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Acknowledgements
The authors would like to thank Ching Hung Lam for valuable discussions. Tomoyuki Arakawa was partially supported by JSPS Grant-in-Aid for Scientific Research No. 25287004, Hiromichi Yamada was partially supported by JSPS Grant-in-Aid for Scientific Research No. 26400040, Hiroshi Yamauchi was partially supported by JSPS Grant-in-Aid for Scientific Research No. 24740027.
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Arakawa, T., Yamada, H., Yamauchi, H. (2016). Vertex Operator Algebras Associated with \(\mathbf{Z}/k\mathbf{Z}\)-Codes. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_38
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DOI: https://doi.org/10.1007/978-981-10-2636-2_38
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