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10: The Moonshine Module

Elsevier B.V.
DOI: 10.1016/s0079-8169(08)62336-3
  • Mathematics


Publisher Summary This chapter discusses the construction of the moonshine module, the associated vertex operator algebra, and the Monster acting on the module and preserving the vertex operator algebra structure. The vertex operator algebra associated with the module, crowns the sequence of exceptional structures starting with the Golay error-correcting code and continuing with the Leech lattice. The corresponding sequence of their automorphism groups consists of the Mathieu group, the Conway group, and the Monster. The chapter discusses binary linear codes and related notions. The Golay code is defined and constructed, and the Mathieu group is defined as its automorphism group. Using the Golay code, the Leech lattice is constructed in the standard way. The chapter also introduces several important lattices related to the Leech lattice, in particular, the Niemeier lattice, and defines the Conway groups.

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