Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z)

2007/11/06 by Oleg Karpenkov, Karpenkov, Oleg · 3 citations
Mathematics · #11H06 #11J70 #15A36 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11H06 #msc:11J70 #msc:15A36

paper · pdf · doi:10.48550/arxiv.0711.0830

29 pages, 4 figures

openalex publication_date 2007/11/06 · arxiv created 2012/05/16 · arxiv updated 2012/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe the set of conjugacy classes in the group SL(n,Z). We expand geometric Gauss Reduction Theory that solves the problem for SL(2,Z) to the multidimensional case. Further we find complete invariant of classes in terms of multidimensional Klein-Voronoi continued fractions, where ς-reduce Hessenberg matrices play the role of reduced matrices.

Cited by

• On Asymptotic Reducibility in SL(3,Z)
• Geometric Continued Fractions as Invariants in the Topological Classification of Anosov Diffeomorphisms of Tori
• The conjugacy problem in GL(n,Z)

Related

• Continued Fraction approach to Gauss Reduction Theory
• On Asymptotic Reducibility in SL(3,Z)
• Gaussian Elimination in Symplectic and split orthogonal groups
• Conjugacy classes in PSL(2, K)
• Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction