Talk:One-parameter group

What about the definition: the set of algebraic group homomorphisms from $\mathbb C^*$ to $G$? 129.215.104.100 (talk) 11:55, 19 September 2012 (UTC)

Usage
The phrase One-parameter group is often used to mean one-dimensional Lie group. At present, this article notes that a particular group homomorphism is being designated by the phrase, so that this particular kind of group is not a group. The structure of a "one-dimensional Lie group" is no different than that of the real line as a group under addition, so its features don't inspire an article. The analysis of the concept presently presented would be confusing to a general reader and verges on meta-mathematics. Given that the topic has a significant literature, there may be sources to fill the vacuum and counter the obfuscation of the non-group group.Rgdboer (talk) 01:04, 10 January 2015 (UTC)

A link to usage by Sophus Lie in 1893 has been posted.Rgdboer (talk) 03:11, 10 January 2015 (UTC)


 * That's definitely a right step. Nice work! -- Taku (talk) 04:01, 10 January 2015 (UTC)


 * The definition (as given in the lead) agrees with all literature I have come across. It is also usually pointed out that it is, in fact, not a group. The topic of this homomorphism does motivate an article imo, while the group $(ℝ, +)$, of course, does not. YohanN7 (talk) 17:31, 10 January 2015 (UTC)

Not a group
"Discussion"

That means that it is not in fact a group, strictly speaking;

That is, we start knowing only that


 * $$\varphi(s+t) = \varphi(s)\varphi(t)$$

where $$s$$, $$t$$ are the 'parameters' of group elements in $$G$$. We may have


 * $$\varphi(s) = e$$, the identity element in $$G$$,

for some $$s \neq 0$$. This happens for example if $$G$$ is the unit circle and


 * $$\varphi(s) = e^{is}_{}$$.

In that case the kernel of $$\varphi$$ consists of the integer multiples of $$2\pi$$.

Therefore a one-parameter group or one-parameter subgroup has to be distinguished from a group or subgroup itself, for the three reasons _______ — Rgdboer (talk) 00:47, 7 March 2019 (UTC)
 * 1) it has a definite parametrization,
 * 2) the group homomorphism may not be injective
 * Much of the "Discussion" is moved here since its only reference is to Stack Exchange, not a WP:Reliable source. Ambiguous use of e is bothersome. Two snippets have been preserved.