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arXiv · 2201.11359

Vertex operator algebras generated by two Ising vectors

Xiangyu Jiao·Wen Zheng
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Abstract

In this paper we mainly study the vertex operator algebra $\mathbb{C} \mathrm{VA}(e, f)$ generated by two Ising vectors $e$ and $f$ with $\langle e, f\rangle=\frac{5}{2^{10}}$. We prove $\mathbb{C} \mathrm{VA}(e, f)$ is isomorphic to the $6A$-algebra $\mathcal{U}_{6A}$ constructed by Lam-Yamada-Yamauchi. We also discuss the cases $\langle e, f\rangle=\frac{1}{4}, \frac{1}{2^{5}}, 0 $ and the case $\langle e, f\rangle=\frac{1}{2^{8}}$ with $(\tau_{e}\tau_{f})^4=1$.

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Xiangyu Jiao, Wen Zheng. 2022-01-27. Vertex operator algebras generated by two Ising vectors. https://arxiv.org/abs/2201.11359

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