INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS

Ching Hung Lam; Hiroki Shimakura

doi:10.1007/s00031-020-09570-8

INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS

Ching Hung Lam, Hiroki Shimakura

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge 24, up to isomorphism, if its weight one Lie algebra has the type C_4,10, D_7,3A_3,1G_2,1, A_5,6C_2,3A_1,2, A_3,1C_7,2, D_5,4C_3,2AA1,12, or E_6,4C_2,1A_2,1. As a consequence, we have verified that the isomorphism class of a strongly regular holomorphic vertex operator algebra of central charge 24 is determined by its weight one Lie algebra structure if the weight one subspace is nonzero.

Original language	English
Pages (from-to)	1223-1268
Number of pages	46
Journal	Transformation Groups
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00031-020-09570-8
Publication status	Published - 2020 Dec 1

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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title = "INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS",

abstract = "We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge 24, up to isomorphism, if its weight one Lie algebra has the type C4,10, D7,3A3,1G2,1, A5,6C2,3A1,2, A3,1C7,2, D5,4C3,2AA1,12, or E6,4C2,1A2,1. As a consequence, we have verified that the isomorphism class of a strongly regular holomorphic vertex operator algebra of central charge 24 is determined by its weight one Lie algebra structure if the weight one subspace is nonzero.",

author = "Lam, {Ching Hung} and Hiroki Shimakura",

note = "Funding Information: C. H. Lam was partially supported by a research grant AS-IA-107-M02 of Academia Sinica and MoST grant 104-2115-M-001-004-MY3 of Taiwan. Funding Information: C. H. Lam and H. Shimakura were partially supported by JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers “Development of Concentrated Mathematical Center Linking to Wisdom of the Next Generation”. Funding Information: H. Shimakura was partially supported by JSPS KAKENHI Grant Numbers 26800001 and 17K05154. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s00031-020-09570-8",

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AU - Shimakura, Hiroki

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N2 - We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge 24, up to isomorphism, if its weight one Lie algebra has the type C4,10, D7,3A3,1G2,1, A5,6C2,3A1,2, A3,1C7,2, D5,4C3,2AA1,12, or E6,4C2,1A2,1. As a consequence, we have verified that the isomorphism class of a strongly regular holomorphic vertex operator algebra of central charge 24 is determined by its weight one Lie algebra structure if the weight one subspace is nonzero.

AB - We continue our program on classiffication of holomorphic vertex operator algebras of central charge 24. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge 24, up to isomorphism, if its weight one Lie algebra has the type C4,10, D7,3A3,1G2,1, A5,6C2,3A1,2, A3,1C7,2, D5,4C3,2AA1,12, or E6,4C2,1A2,1. As a consequence, we have verified that the isomorphism class of a strongly regular holomorphic vertex operator algebra of central charge 24 is determined by its weight one Lie algebra structure if the weight one subspace is nonzero.

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INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS

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