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## 第80回 2017年3月10日 14:00〜15:30

川節 和哉 (Academia Sinica)「$\mathbb{Z}_2$-orbifold construction associated with
$(-1)$-isometry and uniqueness of holomorphic vertex operator algebras
of central charge 24」

Classification of holomorphic vertex operator algebras (VOAs) of
central charge 24 is a fundamental problem in the theory of VOAs.
In 1993, Schellekens obtained a partial classification of holomorphic
VOAs of central charge 24 and showed that there are 71 possible Lie
algebra structures for the weight one spaces of holomorphic VOAs of
central charge 24.
By considering an analogy of the fact that the Niemeier lattices are
determined by their root systems, many researchers have expected that
the holomorphic VOAs of central charge 24 are determined by their
weight one Lie algebras.
In this talk, we show that it is true if the weight Lie algebra 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 $D_{6,2}B_{3,1}^2C_{4,1}$.
Such VOAs are obtained by applying orbifold construction to the
lattice VOAs associated with Niemeier lattices and lifts of
$(-1)$-isometry of the lattices.
This is a joint work with Ching Hung Lam and Xingjun Lin.