An explicit Majorana representation of the group \(3^2:2\) of \(3C\)-pure type

DOI10.2140/PJM.2014.271.25zbMATH Open1323.17020arXiv1305.7306OpenAlexW3099435919MaRDI QIDQ471286

Author name not available (Why is that?)

Publication date: 14 November 2014

Published in: (Search for Journal in Brave)

Abstract: In this article, we study Griess algebras and vertex operator subalgebras generated by Ising vectors in a moonshine type VOA such that the subgroup generated by the corresponding Miyamoto involutions has the shape

3^{2} : 2

and any two Ising vectors generate a 3C subVOA

U_{3 C}

. We show that such a Griess algebra is uniquely determined, up to isomorphisms. The structure of the corresponding vertex operator algebra is also discussed. In addition, we give a construction of such a VOA inside the lattice VOA

V_{E_{8}^{3}}

, which gives an explicit example for Majorana representations of the group

3^{2} : 2

of 3C-pure type.

Full work available at URL: https://arxiv.org/abs/1305.7306

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