Integer Conjugacy Classes of Sl(3, Z) and Hessenberg Matrices. Oleg Karpenkov
نویسنده
چکیده
In this paper we study the problem of description of conjugacy classes in the group SL(n,Z). Gauss Reduction Theory gives the answer for the case n = 2, for n ≥ 3 the problem is still open. We introduce a new approach to this problem based on reduction to reduced Hessenberg matrices. An important tool used in our approach is to determine minima of Markoff-Davenport characteristics at the vertices of Klein-Voronoi continued fractions. Mostly, we work in the case of three-dimensional matrices having a real and two complex-conjugate eigenvalues, nevertheless, the techniques shown in the paper can be applied both to the totally real case and to the multidimensional case.
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