Limits Under Conjugacy of the Diagonal Subgroup in SL(n,R)

2014/12/17 by Arielle Leitner, Leitner, Arielle · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1412.5523

openalex publication_date 2014/12/17 · arxiv created 2015/06/11 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a quadratic lower bound on the dimension of the space of conjugacy classes of subgroups of SL(n,R) that are limits under conjugacy of the diagonal subgroup. We give the first explicit examples of abelian n-1 dimensional subgroups of SL(n,R) which are not such a limit, however all such abelian groups are limits of the diagonal group iff n < 5.

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