AIMS Lie Groups: Fall-2022 Practice Exercises 6 : Due 06 Mon 12 Dec
Bases for $SO(4)$
S0 4486S
Write down the standard basis for the Lie algebra \(\mathfrak{so}(4)\), that is, the infinitesimal rotations in four (Euclidean) dimensions. Note that rotations in orthogonal planes commute. Switch to new basis elements that are the sums and differences of rotations in orthogonal planes. Work out the commutators of these basis elements, showing that \(\mathfrak{so}(4)=\mathfrak{so}(3)\oplus\mathfrak{so}(3)\).