Two commuting rotation algebras in so4
= Two commuting rotation algebras in so4
{title2=$\mathfrak{so}(4)\cong\mathfrak{su}(2)\oplus\mathfrak{su}(2)$}
If $[L_a,L_b]=\epsilon_{abc}L_c$, $[L_a,K_b]=\epsilon_{abc}K_c$ and $[K_a,K_b]=\epsilon_{abc}L_c$, then $L_a^\pm=(L_a\pm K_a)/2$ generate commuting copies of $\mathfrak{su}(2)$. This Lie-algebra decomposition does not remove the central quotient in the corresponding global group.