A Dirichlet approximation theorem for group actions
Abstract
If $G$ is a compact group acting continuously on a compact metric space $(X, m)$, we prove two results that generalize Dirichlet's classical theorem on Diophantine approximation. If $G$ is a noncommutative compact group of isometries, we obtain a noncommutative form of Dirichlet's theorem. We apply our general result to the special case of the unitary group $U(N)$ acting on the complex unit sphere, and obtain a noncommutative result in this setting.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2017
- DOI:
- 10.48550/arXiv.1705.00562
- arXiv:
- arXiv:1705.00562
- Bibcode:
- 2017arXiv170500562P
- Keywords:
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- Mathematics - Number Theory;
- 11J25;
- 37B05;
- 22F10