Talk:Lie group

Too technical?

I see there is a "technical" tag. In my opinion, this article is no more technical than many other math articles and is appropriate for the subject at hand. I am inclined to remove the tag. Or at least I would need a bit of specific information about which part the user feels is overly technical before I could attempt to address the issue. The level seems similar to many introductory textbooks on the subject. — Preceding unsigned comment added by Mathphysman (talk • contribs) 12:29, 16 October 2018 (UTC)

Right. Are there any plausible readers who would want to learn about Lie groups and who would nevertheless find this article too technical? What are the examples of not-too-technical articles on comparably advanced mathematics? Sylvain Ribault (talk) 21:40, 16 October 2018 (UTC)

I'm not going to answer your second question since I don't know the answer, but as for your first question, many physics students will definitely find this article too technical (while trying to learn quantum field theory on their own). It's not quite that any information is missing for them to understand the article, but rather that they will have absolutely no idea what this is talking about until the exponential map is mentioned and they finally notice how matrix groups are Lie groups. At the same time, this article is linked to in a lot of articles on QFT. Qwyxivi (talk) 03:42, 28 September 2019 (UTC)

My sense is that expecting to learn about Lie groups from a QFT study is completely wrong-minded: most physicists learn their su(2) through quantum angular momentum in QM, and generalize to su(3) from a low-level particle physics course. Then they are ready for QFT and the standard model. Personally, whenever I teach this, I spend the first week on remedial group theory, and supplement teaching by reviews and popular physics Lie group books. Physicists are preternatural in learning things by example, monkey-see, monkey-do (I am serious). The idea of coming here for tutorial help is exotic, no? I think the article level is just right. Other WP pages work out the applications that are likely sought. Cuzkatzimhut (talk) 20:45, 28 September 2019 (UTC)

Perhaps including a reference to classical groups in the lede could direct a reader with not enough background to a topic more useful for them? For example the first paragraph could end with something like "An important and fundamental class of Lie groups is given by classical groups such as orthogonal, unitary, symplectic and special linear groups." jraimbau (talk) 08:44, 30 September 2019 (UTC)

Section 2.3 already does that. Cuzkatzimhut (talk) 14:53, 1 October 2019 (UTC)

Yes, but the point would be to put that information up front. jraimbau (talk) 11:03, 2 October 2019 (UTC)

QFT pages are not the only pages that link here. Better examples of pages that link here are Fields Medal and Mathematics. A person with absolutely no knowledge of mathematics is likely to stumble across this page from one of those pages, and will immediate be caught off-guard by the following jargon in the first sentence: "Group", "Differentiable", "Manifold", "Operation". Maybe it is reasonable to expect them to click through to learn what a group is (even then, requiring someone to click through even once just to understand the intro isn't ideal), but I would not expect them to learn what all four of these words mean, just to be able to read the introduction. - Ramzuiv (talk) 05:20, 10 December 2019 (UTC)

I rewrote the lede to minimize the jargon. After that, the next 4-5 paragraphs seem plain enough that ordinary college students should be able to parse their way through them. 67.198.37.16 (talk) 04:17, 11 November 2020 (UTC)

Problems with lede

In the first paragraph, a group whose elements are organized continuously and smoothly, as opposed to discrete groups, where the elements are separated is at best seriously misleading and is certainly confusing; it's a long way from organized to group operations, and there is no dichotomy: one can trivially construct a differentiable manifold with discontinuous group operations.

The second paragraph is better, but needs to mention the smoothness of the group operations and to note that not all topological groups are Lie Groups.

As a side note, I like the suggestion to mention the classical groups in the lede. Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:42, 9 June 2020 (UTC)

I rewrote the lede. I forgot to mention classical groups, I will do that now. 67.198.37.16 (talk) 04:15, 11 November 2020 (UTC)

Wrong link?

From Problem simplication.... 1.46.131.75 (talk) 11:56, 10 April 2022 (UTC)

Projective groups

In #Additional examples, The projective group is confusing. There are distinct types of projective groups, general (full) and special. $\mathrm {PSL} (3,R)\cong \mathrm {SL} (3,\mathbb {R} )$ preserves orientation while $\mathrm {GSL} (3,R)$ does not. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 10:14, 1 June 2022 (UTC)

As written it was pretty useless so i removed it. However it points to a deficiency of the current version of the article, that there the Lie groups ocurring as symmetry groups of differential equations are not mentioned outside of the history section and (not very clearly) the section on representations. This is treated in some detail in the page Lie point symmetry but there should probably be a short paragraph on that here as well; for the time being i added a "see also". jraimbau (talk) 13:33, 1 June 2022 (UTC)

The first example ought to be the circle group

Yes, I believe that this article is too technical for readers interested in this subject, because it doesn't begin with the most obvious starting point for Lie groups: the circle group.

I do not believe there is ever any reason to introduce anyone to Lie groups without beginning with the circle group.