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Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space. It was discovered by . It may also have been discovered (but unpublished) by Ernst Witt in 1940.
==History==
Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than the Leech lattice. discovered a related odd unimodular lattice in 24 dimensions, now called the odd Leech lattice, one of whose two even neighbors is the Leech lattice. The Leech lattice was discovered in 1965 by , by improving some earlier sphere packings he found .
calculated the order of the automorphism group of the Leech lattice, and, working with John G. Thompson, discovered three new sporadic groups as a by-product: the Conway groups, Co1, Co2, Co3. They also showed that four other (then) recently announced sporadic groups, namely, Higman-Sims, Suzuki, McLaughlin, and the Janko group J2 could be found inside the Conway groups using the geometry of the Leech lattice. (Ronan, p. 155)
, has a single rather cryptic sentence mentioning that he found more than 10 even unimodular lattices in 24 dimensions without giving further details. stated that he found 9 of these lattices earlier in 1938, and found two more, the Niemeier lattice with A root system and the Leech lattice (and also the odd Leech lattice), in 1940.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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