# Talk:Cartan matrix

WikiProject Mathematics (Rated Start-class, Mid-importance)
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Mathematics rating:
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Field:  Algebra

There's something wrong with how wikipedia displays this page. There are "Failed to parse" messages all over the article. —Preceding unsigned comment added by 68.0.215.192 (talk) 21:42, 19 January 2009 (UTC)

## M-theory reference out of place?

The section on M theory seems out of place. It describes a recent conjecture in theoretical physics, presumably to promote the hep-th paper [1] it is linking to. Why doesn't wikipedia cite the other 160,000 references google gives us for "hep-th and cartan matrix"? — Preceding unsigned comment added by 78.239.179.184 (talk) 21:59, 11 July 2012 (UTC)

I replaced the arxiv preprint with the published paper. It is cited alright, so it seems legit. (Still, the section may be out of place.) YohanN7 (talk) 23:24, 6 May 2015 (UTC)

## Inconsistent definitions mixed?

In the literature, the Cartan matrix is often defined in a transposed version. In this article, the two definitions seem to have been mixed up. With the definition for simple Lie algebras in terms of the scalar products of roots, the Cartan matrix of G2 should be precisely of what is found on the Wikipedia page for G2, namely the transpose of what is given in the example for the decomposition A=DS. (See e.g. the book of Jacobson on Lie Algebras, p. 121-122.) Point 4 of the definition of the generalized Cartan matrix thus seems inconsistent with the definition of the Cartan matrix of a simple Lie algebra and should be replaced by A=SD, correct? N.Nahber (talk) 13:25, 5 January 2016 (UTC)

PS: I just realized that the two versions of the Cartan matrix for G2 are equivalent for either of the two possible definitions of the Cartan matrix for simple Lie algebras as one only needs to reorder the two simple roots of G2. (This would however not work for the Cartan matrix of B3 whose transpose is that of C3.) But it would certainly be nice to make this page conforming with the Wikipedia page for G2. N.Nahber (talk) N.Nahber (talk) 15:34, 5 January 2016 (UTC)