Diameters of Homogeneous Spaces
Quantum Physics
2007-05-23 v2
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 \beta \approx .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 \geq \beta.
Cite
@article{arxiv.quant-ph/0209113,
title = {Diameters of Homogeneous Spaces},
author = {Michael Freedman and Alexei Kitaev and Jacob Lurie},
journal= {arXiv preprint arXiv:quant-ph/0209113},
year = {2007}
}