Multidimensional Gauss reduction theory for conjugacy classes of \(\mathrm{SL}(n,\mathbb Z)\). (English. French summary) Zbl 1273.11111

Karpenkov, Oleg

J. Théor. Nombres Bordx. 25, No. 1, 99-109 (2013).

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.

Reviewer: Alexey Ustinov (Khabarovsk)

MSC:

11J70	Continued fractions and generalizations
11A55	Continued fractions

Keywords:

special linear group; Gauss reduction theory; multidimensional continued fraction

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