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Indices of Coincidence Isometries of the Hyper Cubic Lattice $Z^n$

Yi Ming Zou
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Abstract

The problem of computing the index of a coincidence isometry of the hyper cubic lattice $\mathbb{Z}^{n}$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain coincidence isometries of $\mathbb{Z}^{n}$ are obtained. These formulas generalize the known results for $n\le 4$.

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Yi Ming Zou. 2006-08-29. Indices of Coincidence Isometries of the Hyper Cubic Lattice $Z^n$. https://arxiv.org/abs/math/0608732

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