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I would like to find effectively the Cartan subalgebra of ${\frak so}(5)$. Does anybody knows how to proceed?

Edit: I don't want to start from the simple roots and then derive it. I would like to do the pedagogical procedure, starting from the cartan subalgebra and identifying the simple roots.

Dac0
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1 Answers1

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For the Cartan subalgebra of $B_2$ (in fact, for all classical simple Lie algebras), see this handout. Here $B_2$ is the root system of $\mathfrak{so}(5)$.

Dietrich Burde
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  • do you also have a place where are written some standard procedure to identify the cartan subalgebra? – Dac0 Feb 13 '16 at 21:34
  • If $\mathfrak{g}$ is a linear Lie algebra over an algebraically closed field, then any Cartan subalgebra of $\mathfrak{g}$ is the centralizer of a maximal toral Lie subalgebra of $\mathfrak{g}$. There are many standard references, some of them given here. – Dietrich Burde Feb 13 '16 at 21:38