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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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##### References:
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