dorsal/arxiv
View SchemaDiameters of Homogeneous Spaces
| Authors | Michael Freedman, Alexei Kitaev, Jacob Lurie |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209113 |
| URL | https://arxiv.org/abs/quant-ph/0209113 |
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.
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"abstract": "Let G be a compact connected Lie group with trivial center. Using the action\nof G on its Lie algebra, we define an operator norm | |_{G} which induces a\nbi-invariant metric d_G(x,y)=|Ad(yx^{-1})|_{G} on G. We prove the existence of\na constant \\beta \\approx .12 (independent of G) such that for any closed\nsubgroup H \\subsetneq G, the diameter of the quotient G/H (in the induced\nmetric) is \\geq \\beta.",
"arxiv_id": "quant-ph/0209113",
"authors": [
"Michael Freedman",
"Alexei Kitaev",
"Jacob Lurie"
],
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"quant-ph"
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"title": "Diameters of Homogeneous Spaces",
"url": "https://arxiv.org/abs/quant-ph/0209113"
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