Timeline for Normalising Generators of a Lie Algebra

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May 3, 2015 at 18:07	comment	added	Jojo		Oh so you did, yes that makes more sense then. Ok thanks I will have a read of that
May 3, 2015 at 17:06	comment	added	joshphysics		@Joe The definition above gives an inner product on any real or complex vector space of square matrices. It is commonly called the Frobenius or Hilbert-Schmidt inner product. Naturalness comes from thinking of matrices as rearranged column vectors and then applying the standard inner product on $\mathbb C^{n^2}$. See en.wikipedia.org/wiki/Matrix_multiplication#Frobenius_product . Note that I wrote norm-squared $1/2$.
May 3, 2015 at 0:42	comment	added	Jojo		Ok that's helpful, thanks. So is this inner product only standard for $\mathfrak{su}(N)$, or in general for any Lie algebra? Because if it's only standard for $\mathfrak{su}(N)$, why is it defined with the Hermitian conjugate if you're then going to get rid of that anyway? And why is it natural to define this to be our inner product? Also presumably when you say that the vectors have norm $\frac{1}{2}$, you mean $\frac{1}{\sqrt{2}}$?
May 3, 2015 at 0:40	vote	accept	Jojo
May 1, 2015 at 19:28	history	answered	joshphysics	CC BY-SA 3.0