Talk:Root system

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Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	A-BB+ Class	High 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. This may even be A-class. Arcfrk 07:46, 23 May 2007 (UTC) At a glance, it needs more references and motivation. Geometry guy 22:49, 9 June 2007 (UTC)

Any particular reason for removing

• Simply connected compact Lie groups which are simple modulo their centers?

Michael Larsen 11:39, 24 Oct 2003 (UTC)

I've merged in now what was on Dynkin diagram. I think that - and then moving out the Dynkin diagrams from the simple Lie group page - is much preferable to merging the latter here.

Charles Matthews 17:43, 3 Dec 2003 (UTC)

[edit] Root systems and Lie theory

I think, it would be good to have more specific information on the classification of simple complex Lie groups and / or "Simply connected complex Lie groups which are simple modulo centers". Perhaps an extra page for these classifications issues?

Perhaps it would be an idea to delete the link to "Simple Lie-Algebra" in this section, as it redirects to "Simple Lie groups"?

[edit] One comment

I believe that there should be a mention to the other way of drawing Dynkin diagrams - that is, with single edges everywhere and numbers indicating the angle. Regards --132.205.159.206 19:20, 5 May 2006 (UTC)

[edit] In the news

Does the following article relate to this page?

• NPR: "Team Solves Mammoth, Century-Old Math Problem": "Scientists have solved one of the toughest problems in mathematics, performing a calculation to figure out the symmetry of a 248-dimensional object known as the Lie group E8."

— Chris53516 ^(Talk) 15:06, 23 March 2007 (UTC)

[edit] Positive definite

This article references the term positive definite, which is a disambiguation page. Please review this usage and determine which of the articles at the disambiguation is intended and adjust as appropriate. Chromaticity 02:25, 7 May 2007 (UTC)

• Done. It was referring to an inner product, which is a bilinear form. Though, I believe that since this article is only talking about Euclidean spaces, any of the three definitions of "positive definite" would apply. 66.117.137.139 (talk) 23:01, 17 November 2007 (UTC)

[edit] Question

The article says: "The set of simple roots is a subset Δ of Φ which is a basis of V with the special property that every vector in Φ when written in the basis Δ has either all coefficients ≥0 or else all ≤0.". However, I think there is a mistake, because that is not possible. For example, for a root α in Δ, the root − α may never has a coefficient ≥0 in a basis of V. —Preceding unsigned comment added by 88.24.73.176 (talk) 09:17, 22 September 2007 (UTC)

If Δ = (α₁,...α_i,...α_n), then the root -α_i has coordinates (0,...0,-1,0...0) in the basis Δ, whose coefficients are all ≤0. --JWB 12:11, 22 September 2007 (UTC)

You are totally right. I misread that either all roots had coefficients ≥0 or all roots had coefficients ≤0. Sorry for my english. —Preceding unsigned comment added by 88.23.98.119 (talk) 14:10, 23 September 2007 (UTC)

[edit] Lie groups in "most parts of mathematics"?

What's the basis for the claim that "Lie groups... have come to be used in most parts of mathematics"? What does that even mean? Is it saying that more than 50% of the world's current professional mathematicians use Lie groups in their daily work? More than 50% of all articles published in peer-reviewed mathematical journals mention Lie groups? I doubt that either of these is actually true. 66.117.137.139 (talk) 22:38, 17 November 2007 (UTC)