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Abstract: In this article, we study the moonshine vertex operator algebra starting withthe tensor product of three copies of the vertex operator algebra$V {\sqrt2E 8}^+$, and describe it by the quadratic space over $\F 2$associated to $V {\sqrt2E 8}^+$. Using quadratic spaces and orthogonal groups,we show the transitivity of the automorphism group of the moonshine vertexoperator algebra on the set of all full vertex operator subalgebras isomorphicto the tensor product of three copies of $V {\sqrt2E 8}^+$, and determine thestabilizer of such a vertex operator subalgebra. Our approach is a vertexoperator algebra analogue of -An $E 8$-approach to the Leech lattice and theConway group- by Lepowsky and Meurman. Moreover, we find new analogies amongthe moonshine vertex operator algebra, the Leech lattice and the extendedbinary Golay code.



Author: Hiroki Shimakura

Source: https://arxiv.org/







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