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2021 Fourvolutions and Automorphism Groups of Orbifold Lattice Vertex Operator Algebras
Hsian-Yang Chen, Ching Hung Lam
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Taiwanese J. Math. Advance Publication 1-13 (2021). DOI: 10.11650/tjm/210502

Abstract

Let $L$ be an even positive definite lattice with no roots, i.e., $L(2) = \{ x \in L \mid (x|x) = 2 \} = \emptyset$. Let $g \in O(L)$ be an isometry of order $4$ such that $g^2 = -1$ on $L$. In this article, we determine the full automorphism group of the orbifold vertex operator algebra $V_L^{\widehat{g}}$. As our main result, we show that $\operatorname{Aut}(V_L^{\widehat{g}})$ is isomorphic to $N_{\operatorname{Aut}(V_L)}(\langle \widehat{g} \rangle)/\langle \widehat{g} \rangle$ unless $L \cong \sqrt{2} E_8$ or $BW_{16}$.

Funding Statement

Chen is supported by MOST grant 109-2115-M-024-005-MY2 of Taiwan. Lam is supported by a research grant AS-IA-107-M02 of Academia Sinica and MOST grant 107-2115-M-001-003-MY3 of Taiwan.

Citation

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Hsian-Yang Chen. Ching Hung Lam. "Fourvolutions and Automorphism Groups of Orbifold Lattice Vertex Operator Algebras." Taiwanese J. Math. Advance Publication 1 - 13, 2021. https://doi.org/10.11650/tjm/210502

Information

Published: 2021
First available in Project Euclid: 24 May 2021

Digital Object Identifier: 10.11650/tjm/210502

Subjects:
Primary: 17B69

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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