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Multidimensional Gauss reduction theory for conjugacy classes of \(\mathrm{SL}(n,\mathbb Z)\). (English. French summary) Zbl 1273.11111
The author describes the set of conjugacy classes in the group \(mathrm{SL}(n,\mathbb{Z})\). He expands geometric Gauss Reduction Theory that solves the problem for \(mathrm{SL}(n,\mathbb{Z})\) to the multidimensional case, where \(\zeta\)-reduced Hessenberg matrices play the role of reduced matrices. He also describes complete invariants of conjugacy classes in \(mathrm{SL}(n,\mathbb{Z})\) in terms of multidimensional Klein-Voronoi continued fractions.
MSC:
11J70 Continued fractions and generalizations
11A55 Continued fractions
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