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Genus of vertex algebras and mass formula

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We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which play an important role in the classification of lattices. We derive a formula relating the mass for vertex algebras to that for lattices, and then give a new characterization of some holomorphic vertex operator algebras.

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Acknowledgements

The author would like to express his gratitude to Professor Atsushi Matsuo, for his encouragement throughout this work and numerous advices to improve this paper. He is also grateful to Hiroki Shimakura and Shigenori Nakatsuka for careful reading of this manuscript and their valuable comments. This work was supported by the Program for Leading Graduate Schools, MEXT, Japan.

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  1. Graduate School of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Yuto Moriwaki

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  1. Yuto Moriwaki
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Correspondence to Yuto Moriwaki.

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Moriwaki, Y. Genus of vertex algebras and mass formula. Math. Z. 299, 1473–1505 (2021). https://doi.org/10.1007/s00209-021-02702-0

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