Show that $\mathfrak{so}(4) \simeq \mathfrak{su}(2) \oplus \mathfrak{su}(2)$.
How do I proceed to show that it is true?
I know that the basis of $\mathfrak{su}(2)$ is the Pauli-matrices multiplied by i. I really don't know what to do next.
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3Are you familiar with the isomorphism $\mathfrak{su}(2)\cong\mathfrak{so}(3)$? – Kajelad Nov 11 '20 at 00:53
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2Fun fact: If you interpret the parameters $a,...,f$ in the answer to https://math.stackexchange.com/q/3708404/96384 as real numbers (instead of the complex numbers used there), you are ... done. – Torsten Schoeneberg Nov 11 '20 at 01:24
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See your question here. – Dietrich Burde Nov 11 '20 at 17:43