Talk:SL2(R)

message: I noticed that there wasn't an article on this subject, so I went ahead and made one, mostly because there ought to be some article discussing the hyperbolic/parabolic/elliptic trichotomy.  It could use a better summary of the representation theory, more details on the algebraic structure, and a discussion on the relationship to moduli space. Jim 07:29, 25 July 2007 (UTC)
replies: text: I changed the wording. It now says that elements of SL2 preserve "oriented area", with links to orientation (mathematics) and area (geometry).  There really ought to be an article on oriented area or signed area.  Jim 03:37, 18 August 2007 (UTC)
thread_title: Untitled

message: Why is this at SL₂(R) and not SL(2, R) or similar? The former breaks two guidelines in the naming conventions, namely
* Use italics but "Other types of formatting (bold type, superscript, etc.) [...] should not be used in Wikipedia article titles."
* Do not use non-language characters: Non-language characters such as "♥", as sometimes found in advertisements or logos, should never be used in titles.
The current title is a subscript, in breach of the former guideline, then uses a very non-standard way to do it so breaches the second. The use of special Unicode subscripts is also against the Math MOS, for reasons given here. It's also not used anywhere in the article, and surely the article title should match the lede and rest of the article?--JohnBlackburnewordsdeeds 17:41, 16 October 2010 (UTC)
replies: text: I tend to agree:  The article should be at SL(2, R) (except we would have an edit war about the spacing) or SL2(R) displayed SL2(R).  — Arthur Rubin  (talk) 19:19, 16 October 2010 (UTC)
replies: text:  Agreed.  The second option seems best. CRGreathouse (t | c) 19:37, 16 October 2010 (UTC)
replies: text: I moved it. Ozob (talk) 21:27, 16 October 2010 (UTC)
replies: text: That's better, though it still did not match the text so I've added it. It still seems odd that the name as used in the title doesn't match the bulk of the article, but the various issues wrt the naming conventions are fixed.--JohnBlackburnewordsdeeds 22:21, 16 October 2010 (UTC)

text: And the reason it doesn't match the text is that there might be an edit war about a space in the name? I think it might do me some good to get myself some bubble wrap so I can pop a few bubbles on occasions like this :) 86.9.212.44 (talk) 22:48, 16 October 2010 (UTC)

text: If you told me that "₂" is a "non-language character", then how can "SL" and "R" be "language character"? Then the title would be better moved to Special Linear group (Real) degree 2. ––<Span xml:lang="zh" lang="zh">虞海</Span> (Yú Hǎi) (talk) 05:32, 17 October 2010 (UTC)
replies: text: A "non-language character" is a character that is not normally used in the language.  The parentheses are questionable, but "S", "L", and "R" are not "non-language characters".  I reverted your move, and am deleting the "Special Linear group (Real) ..." files.  — Arthur Rubin  (talk) 07:34, 17 October 2010 (UTC)
replies: text:  That's merely an imposing on the definition. If such imposing may be accepted, "₂" will also be a language character, for its no difference from the number ₂! ––<Span xml:lang="zh" lang="zh">虞海</Span> (Yú Hǎi) (talk) 07:45, 17 October 2010 (UTC)
replies: text: This is an English language encyclopaedia and one of the more desirable things is that English readers be able to easily write the title of an article in the search box. That's why there is that naming convention. Occasionally there are problems without a simple solution where one needs a character not on an English keyboard but this article is obviously not one of them. Dmcq (talk) 13:24, 17 October 2010 (UTC)
replies: text:  It is a desirable things for writers but not for readers. Writers should always think of readers. So the look-and-feel is more important. For the title, we can simply made redirection to "lead" the readers to the correct article. ––<Span xml:lang="zh-Hant-CN" lang="zh-Hant">虞海</Span> (Yú Hǎi) (talk) 13:43, 17 October 2010 (UTC)
replies: text: Please follow the naming conventions or else discuss this there and get them changed first. This article does not need a change from them so should only be changed if the conventions say that is desirable. Dmcq (talk) 14:11, 17 October 2010 (UTC)
thread_title:  Article name 

message: Substituted at 02:34, 5 May 2016 (UTC)
thread_title: Assessment comment

message: The section Möbius transformations begins as follows:
"Elements of PSL(2, R) act on the complex plane by Möbius transformations:
: z \mapsto \frac{az+b}{cz+d}\;\;\;\;\mbox{ (where }a,b,c,d\in\mathbf{R}\mbox{)}.
"This is precisely the set of Möbius transformations that preserve the upper half-plane."
But if a = -1, b = 0 = c, and d = 1  we get the Möbius transformation z \mapsto -z, which does not preserve the upper half-plane. 
It's necessary to impose the condition that ad-bc = 1 to avoid this kind of thing.
Of course, we're talking about SL(2,R) and PSL(2,R), so maybe ad-bc = 1 is always assumed.
But it doesn't hurt to mention it again. 2601:200:C000:1A0:C9BF:3229:6680:A9F6 (talk) 22:52, 21 December 2022 (UTC)
thread_title:  Is this right?