正定格的分类
Classification of positive definite lattices
摘要：
在本文中，我们描述了一个算法分类的轨道向量的洛伦兹格。其主要观点是正定格在某亏格上的同构类往往对应于某Lorentz格上的向量轨道，从而可以对某些正定格进行分类。作为应用，我们给出了行列式2的665个25维单模正定格和121个偶数25维正定格的分类。我们还利用这个算法证明了存在唯一的无根26维么模正定格。
英文摘要：
In this paper we describe an algorithm for classifying orbits of vectors in Lorentzian lattices. The main point of this is that isomorphism classes of positive definite lattices in some genus often correspond to orbits of vectors in some Lorentzian lattice, so we can classify some positive definite lattices. As an application we give the classification of the 665 25-dimensional unimodular positive definite lattices and the 121 even 25 dimensional positive definite lattices of determinant 2. We also use this algorithm to show that there is a unique 26 dimensional unimodular positive definite lattice with no roots.
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