Diameters of Homogeneous Spaces
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2002
- DOI:
- 10.48550/arXiv.quant-ph/0209113
- arXiv:
- arXiv:quant-ph/0209113
- Bibcode:
- 2002quant.ph..9113F
- Keywords:
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- Quantum Physics