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

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

2006-08-29

arxiv.org/abs/math/0608732v1

Mathematics

Group Theory

AMS-Latex, preprint 10 pages

Scientific paper

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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