Multidimensional Gauss reduction theory for conjugacy classes of $\mathrm{SL}(n,\mathbb{Z})$
作者: Oleg Karpenkov
刊名: Journal de théorie des nombres de Bordeaux, 2013, Vol.25 (1), pp.99-109
来源数据库: The Center for Diffusion of Academic Mathematical Journals
DOI: 10.5802/jtnb.828
原始语种摘要: In this paper we describe the set of conjugacy classes in the group ${\mathord {\rm SL}}(n,\mathbb{Z})$. We expand geometric Gauss Reduction Theory that solves the problem for ${\mathord {\rm SL}}(2,\mathbb{Z})$ to the multidimensional case, where $\varsigma $-reduced Hessenberg matrices play the role of reduced matrices. Further we find complete invariants of conjugacy classes in ${\mathord {\rm GL}}(n,\mathbb{Z})$ in terms of multidimensional Klein-Voronoi continued fractions.
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  • 术语 题目
  • conjugacy 共轭性
  • Gauss 高斯
  • reduced 减缩的
  • reduction 减少
  • matrices 基体
  • geometric 凡何
  • complete 实行
  • where 哪里
  • problem 题目
  • terms 题目