ℤ₂-orbifold construction associated with (-1)-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24

Kawasetsu, Kazuya; Lam, Ching Hung; Lin, Xingjun

doi:10.1090/proc/13881

$\mathbb {Z}_2$-orbifold construction associated with $(-1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24
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by Kazuya Kawasetsu, Ching Hung Lam and Xingjun Lin PDF

Proc. Amer. Math. Soc. 146 (2018), 1937-1950 Request permission

Abstract:

The vertex operator algebra structure of a strongly regular holomorphic vertex operator algebra $V$ of central charge $24$ is proved to be uniquely determined by the Lie algebra structure of its weight one space $V_1$ if $V_1$ is a Lie algebra of the type $A_{1,4}^{12}$, $B_{2,2}^6$, $B_{3,2}^4$, $B_{4,2}^3$, $B_{6,2}^2$, $B_{12,2}$, $D_{4,2}^2B_{2,1}^4$, $D_{8,2}B_{4,1}^2$, $A_{3,2}^4A_{1,1}^4$, $D_{5,2}^2A_{3,1}^2$, $D_{9,2}A_{7,1}$, $C_{4,1}^4$, or $D_{6,2}B_{3,1}^2C_{4,1}$.

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