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The automorphism group of the ${\mathbb Z}_2$-orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32

Published online by Cambridge University Press:  09 January 2014

HIROKI SHIMAKURA
HIROKI SHIMAKURA*
Affiliation:
Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Aramaki aza Aoba 6-3-09, Aoba-ku Sendai-city, 980-8579, Japan. e-mail: shimakura@m.tohoku.ac.jp
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Abstract

In this paper, we prove that the full automorphism group of the ${\mathbb Z}_2$-orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32 has the shape 227.E6(2). In order to identify the group structure, we introduce a graph structure on the Griess algebra and show that it is a rank 3 graph associated to E6(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 2 , March 2014 , pp. 343 - 361
Copyright
Copyright © Cambridge Philosophical Society 2014 

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