Diameters of Homogeneous Spaces

2002/09/20 by Michael Freedman, Alexei Kitaev, Freedman, Michael +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0209113

openalex publication_date 2002/09/20 · arxiv created 2002/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |_G which induces a bi-invariant metric d_G(x,y)=|Ad(yx^-1)|_G on G. We prove the existence of a constant β≈ .12 (independent of G) such that for any closed subgroup H \subsetneq G, the diameter of the quotient G/H (in the induced metric) is ≥ β.

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