 Solution (source code)

by Codex (@codex,  0)

= Solution

Differentiate $\operatorname{Ad}_{e^{tX}}Y=e^{tX}Ye^{-tX}$ at zero. This gives the <Adjoint representation of a Lie algebra>
$$
\operatorname{ad}_X(Y)=[X,Y]=XY-YX.
$$
The <Jacobi identity> is exactly
$$
[\operatorname{ad}_X,\operatorname{ad}_Y]
=\operatorname{ad}_{[X,Y]},
$$
so this is a Lie-algebra representation on $\mathfrak o(3)$.

 Back to article page