# Tagged Questions

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### Do the Generalized Gell-Mann Matrices form a complete set?

Please bear with me, I'm studying Lie algebras as they are related to quantum mechanics, and most of my group theory knowledge is self-taught. I'm not sure how to prove this seemingly basic result. ...
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### How to build a basis for a vector space E(n+1) from a set of points given in E(n) (a vector space of rank n).

I'm interested in how (and if) one can build a new dimension from a set of given dimensions. Specifically, if we are given a vector space E(n) of rank n, and a sample S of elements of E(n) (let us ...
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### Show that V $\otimes _\mathbb{R}$ $\mathbb{C}$ is isomorphic to V + iV

Let V be a real n-dimensional vector space. Show that V $\otimes _\mathbb{R}$ $\mathbb{C}$ is isomorphic to V + iV. Note that V $\otimes _\mathbb{R}$ $\mathbb{C}$ is a real vector space and is ...
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### Representations of Direct Sum of Lie Algebras

I'm trying to prove the following. Let $\frak{g}$ and $\frak{h}$ be (semisimple) Lie algebras. Then every representation $d$ of $\frak{g}\oplus\frak{h}$ is the tensor product of representations $d^1$ ...
### Action of $\mathfrak{sl}({V})$ in tensor spaces
what is the natural action of $\mathfrak{sl}({V})$ in tensor spaces ?
Let $\sigma_0,\sigma_x,\sigma_y,\sigma_z$ stand for the $2\times 2$ identity matrix and the well known pauli matrices: ...