Talk:SL2(R)

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Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Start Class	Low Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs better references, and more on the algebraic structure and representation theory. Jim 06:23, 10 August 2007 (UTC)

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)

The page says SL2(R) consists of all area-preserving 2x2 matrices. But if det(A)=-1 then A is also area-preserving. So this needs an additional caveat. I'm not quite sure how to phrase it without messing up the discourse with something too tangential. "...that preserve clockwiseness" seemed awkwards. Barak 10:28, 17 August 2007 (UTC)

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)