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In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in ''n''-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1. The ''E''8 lattice and the Leech lattice are two famous examples. == Definitions == * A lattice is a free abelian group of finite rank with a symmetric bilinear form (·,·). * The lattice is integral if (·,·) takes integer values. * The dimension of a lattice is the same as its rank (as a Z-module). * The norm of a lattice element ''a'' is (''a'', ''a''). * A lattice is positive definite if the norm of all nonzero elements is positive. * The determinant of a lattice is the determinant of the Gram matrix, a matrix with entries ''(ai, aj)'', where the elements ''ai'' form a basis for the lattice. * An integral lattice is unimodular if its determinant is 1 or −1. * A unimodular lattice is even or type II if all norms are even, otherwise odd or type I. * The minimum of a positive definite lattice is the lowest nonzero norm. * Lattices are often embedded in a real vector space with a symmetric bilinear form. The lattice is positive definite, Lorentzian, and so on if its vector space is. * The signature of a lattice is the signature of the form on the vector space. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Unimodular lattice」の詳細全文を読む スポンサード リンク
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