# Talk:One-parameter group

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Field:  Geometry

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)