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Vertex operator algebras associated to the Virasoro algebra over an arbitrary field


Authors: Chongying Dong and Li Ren
Journal: Trans. Amer. Math. Soc. 368 (2016), 5177-5196
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/tran/6529
Published electronically: November 12, 2015
MathSciNet review: 3456176
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Abstract: The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field $ \mathbb{F}$ with $ \mathrm {ch}\mathbb{F}\ne 2$ are studied. The irreducible modules of vertex operator algebra $ L(\frac {1}{2},0)_{\mathbb{F}}$ are classified. The rationality of $ L(\frac {1}{2},0)_{\mathbb{F}}$ is established if $ \mathrm {ch}\mathbb{F}\ne 7.$


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Additional Information

Chongying Dong
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China — and — Department of Mathematics, University of California, Santa Cruz, California 95064

Li Ren
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China

DOI: https://doi.org/10.1090/tran/6529
Received by editor(s): March 31, 2014
Received by editor(s) in revised form: July 20, 2014
Published electronically: November 12, 2015
Additional Notes: The first author was supported by an NSF grant and China NSF grant 11371261
The second author was supported in part by China Postdoctor grant 2012M521688 and China NSF grant 11301356
Article copyright: © Copyright 2015 American Mathematical Society