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February 2016 Vertex operator algebras with central charge 1/2 and $-68/7$
Kiyokazu Nagatomo, Yuichi Sakai
Proc. Japan Acad. Ser. A Math. Sci. 92(2): 33-37 (February 2016). DOI: 10.3792/pjaa.92.33

Abstract

In this article we study \textit{simple vertex operator algebras} whose spaces of characters are 3-dimensional, and satisfy \textit{3rd order (modular) linear differential equations}. We classify such vertex operator algebras with central charge 1/2 or $-68/7$. One of the main results is that these vertex operator algebras have \textit{conformal weights} $\{0,1/2,1/16\}$ or $\{0,-2/7,-3/7\}$, respectively, and are isomorphic to the minimal models of central charge $c=c_{3,4}=1/2$ and $c_{2,7}=-68/7$. Moreover, we give the explicit formulas representing characters of the minimal models with $c=1/2$, $-68/7$ by using the classical Weber functions.

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Kiyokazu Nagatomo. Yuichi Sakai. "Vertex operator algebras with central charge 1/2 and $-68/7$." Proc. Japan Acad. Ser. A Math. Sci. 92 (2) 33 - 37, February 2016. https://doi.org/10.3792/pjaa.92.33

Information

Published: February 2016
First available in Project Euclid: 28 January 2016

zbMATH: 1370.17027
MathSciNet: MR3455133
Digital Object Identifier: 10.3792/pjaa.92.33

Subjects:
Primary: 11F11 , 81T40
Secondary: 17B69

Keywords: classification of vertex operator algebras , vertex operator algebras

Rights: Copyright © 2016 The Japan Academy

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Vol.92 • No. 2 • February 2016
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