# A vertex operator algebra related to E8 with automorphism group O+(10, 2)

@inproceedings{Griess2008AVO,
title={A vertex operator algebra related to E8 with automorphism group O+(10, 2)},
author={Robert L. Griess},
year={2008}
}
We study a particular VOA which is a subVOA of the E8-lattice VOA and determine its automorphism group. Some of this group may be seen within the group E8(C), but not all of it. The automorphism group turns out to be the 3-transposition group O(10, 2) of order 2357.17.31 and it contains the simple group Ω(10, 2) with index 2. We use a recent theory of Miyamoto to get involutory automorphisms associated to conformal vectors. This VOA also embeds in the moonshine module and has stabilizer in M I…

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## References

SHOWING 1-6 OF 6 REFERENCES
Elementary abelian p-subgroups of algebraic groups
AbstractLet $$\mathbb{K}$$ be an algebraically closed field and let G be a finite-dimensional algebraic group over $$\mathbb{K}$$ which is nearly simple, i.e. the connected component of the
Simple groups of Lie type
Partial table of contents: The Classical Simple Groups. Weyl Groups. Simple Lie Algebras. The Chevalley Groups. Unipotent Subgroups. The Diagonal and Monomial Subgroups. The Bruhat Decomposition.
On finite simple subgroups of the complex Lie group of type $E_8$
• Mathematics
• 1987
• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published
Griess , Jr . , On finite simplesubgroups of the complex Lie group of type E 8
• Proc . Comm . Pure Math .
• 1989
A subgroup of order 215|GL(5
• J. of Algebra
• 1976