European Journal of Mathematics https://doi.org/10.1007/s40879-018-0257-6 RESEARCH ARTICLE 1,2 3,4 Chongying Dong · Ching Hung Lam · Li Ren Received: 12 September 2017 / Revised: 7 April 2018 / Accepted: 18 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract Framed vertex operator algebras over any algebraically closed ﬁeld whose characteristic is different from 2 and 7 are studied. In particular, the rationality of framed vertex operator algebras is established. For a code vertex operator algebra, the irreducible modules are constructed and classiﬁed. Moreover, a Z[ /2]-form for any framed vertex operator algebra over C is constructed. As a result, one can obtain a modular framed vertex operator algebra from any framed vertex operator algebra over C. Keywords Vertex operator algebras · Modular representation · Integral forms Mathematics Subject Classiﬁcation 17B69 CD was supported by the NSF Grant DMS-1404741. CHL was partially supported by the MoST Grant 104-2115-M-001-004-MY3 of Taiwan. LR was supported by the China NSF Grant 11301356. Li Ren renl@scu.edu.cn Chongying Dong dong@ucsc.edu Ching Hung Lam chlam@math.sinica.edu.tw School of Mathematics, Sichuan University, Chengdu 610064, China Department of Mathematics, University of California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA Institute of Mathematics,
European Journal of Mathematics – Springer Journals
Published: May 31, 2018
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