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INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS

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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, D5,4C3,2A\( {A}_{1,1}^2 \), 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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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica and National Center for Theoretical Sciences of Taiwan, Taipei, 10617, Taiwan

    CHING HUNG LAM

  2. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    HIROKI SHIMAKURA

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  1. CHING HUNG LAM
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Correspondence to CHING HUNG LAM.

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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.

H. Shimakura was partially supported by JSPS KAKENHI Grant Numbers 26800001 and 17K05154.

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”.

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LAM, C.H., SHIMAKURA, H. INERTIA GROUPS AND UNIQUENESS OF HOLOMORPHIC VERTEX OPERATOR ALGEBRAS. Transformation Groups 25, 1223–1268 (2020). https://doi.org/10.1007/s00031-020-09570-8

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