On nth roots and infinitely divisible elements in a connected Lie group
Published online by Cambridge University Press: 24 October 2008
Extract
For any group G, x ∈ G and n ∈ ℕ (the natural numbers), let
i.e. the set of all nth roots of x in G. If G is a Hausdorff topological group, then Rn(x, G) is a closed set in G, but may otherwise be quite complicated. However, as we have observed in (4), if G is a compact Lie group, then Rn(x, G) always has a finite number of connected components, and this result has led us to wonder about the connectedness properties of Rn(x, G) for other Lie groups G. Here is the result.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 293 - 299
- Copyright
- Copyright © Cambridge Philosophical Society 1981
References
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