TY - JOUR

T1 - Classification of vertex operator algebras of class S4 with minimal conformal weight one

AU - Maruoka, Hiroyuki

AU - Matsuo, Atsushi

AU - Shimakura, Hiroki

N1 - Funding Information:
The second author was partially supported by JSPS KAKENHI Grant Number 26610004. The third author was partially supported by JSPS KAKENHI Grant Numbers 23540013 and 26800001, as well as by Grant for Basic Science Research Projects from The Sumitomo Foundation. The authors wish to thank Hisayoshi Matsumoto for helpful comments. They also wish to thank the referee for useful comments and valuable suggestions.
Publisher Copyright:
©2016 The Mathematical Society of Japan.

PY - 2016

Y1 - 2016

N2 - In this article, we describe the trace formulae of composition of several (up to four) adjoint actions of elements of the Lie algebra of a vertex operator algebra by using the Casimir elements. As an application, we give constraints on the central charge and the dimension of the Lie algebra for vertex operator algebras of class S4. In addition, we classify vertex operator algebras of class S4 with minimal conformal weight one under some assumptions.

AB - In this article, we describe the trace formulae of composition of several (up to four) adjoint actions of elements of the Lie algebra of a vertex operator algebra by using the Casimir elements. As an application, we give constraints on the central charge and the dimension of the Lie algebra for vertex operator algebras of class S4. In addition, we classify vertex operator algebras of class S4 with minimal conformal weight one under some assumptions.

KW - Deligne's exceptional Lie algebras

KW - Trace formula

KW - Vertex operator algebra

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U2 - 10.2969/jmsj/06841369

DO - 10.2969/jmsj/06841369

M3 - Article

AN - SCOPUS:84992491322

VL - 68

SP - 1369

EP - 1388

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 4

ER -