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II25,1
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II25,1 : ウィキペディア英語版
II25,1

In mathematics, II25,1 is the even 26-dimensional Lorentzian unimodular lattice. It has several unusual properties, arising from Conway's discovery that it has a norm zero Weyl vector. In particular it is closely related to the Leech lattice, and has the Conway group Co1 at the top of its automorphism group.
==Construction==

Write ''R''m,n for the ''m+n'' dimensional vector space
''R''m+n with the inner product of
(''a''1,...,''a''m+n) and (''b''1,...,''b''m+n) given by
:''a''1''b''1+...+''a''m''b''m − ''a''m+1''b''m+1 − ... − ''a''m+n''b''m+n.
The lattice ''II25,1'' is given by all vectors (''a''1,...,''a''26)
in ''R''25,1 such that either all the ''ai'' are integers or they are all integers
plus 1/2, and their sum is even.

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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