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The Automorphism Group of the Hamming Code Vertex Operator Algebra

โœ Scribed by Atsushi Matsuo; Mika Matsuo

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
163 KB
Volume
228
Category
Article
ISSN
0021-8693

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We study a set of certain automorphisms of the Hamming code vertex operator algebra M , which permute the three sets of conformal vectors. We call this set H 8 the triality of H . We construct an embedding M to the VOA V associated to H H D 8 8 4 the lattice of type D , and we establish that the tri

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## DEDICATED TO PROFESSOR MICHIO SUZUKI ON HIS 70TH BIRTHDAY โฃqD D ลฝ . Condition S M = U is irreducible for any irreducible M -mod-โฃqD D ule U. Here M = U denotes a fusion product or a tensor product. They โฃqD both are the same in this paper since we will treat only rational VOAs. As

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In this article, we obtain a decomposition of the Moonshine vertex operator h ลฝ ลฝ . ลฝ . ลฝ .. m12 algebra V associated with the algebra L 1r2, 0 m L 7r10, 0 m L 4r5, 0 . Our method is based on a coset decomposition of the Leech lattice โŒณ associated 12 ' ลฝ . with 2 A using some codes. In fact, we cons