= Killing frame for a right-invariant Heisenberg metric
{title2=$\partial_x,\partial_y+x\partial_z,\partial_z$}
Every <right-invariant Riemannian metric> on the <Heisenberg group> has <Killing vector fields> $\partial_x$, $\partial_y+x\partial_z$ and $\partial_z$. Their <Lie brackets of vector fields> reproduce $[X,Y]=Z$ and the central relations. Their flows are right translations. The dual frame of the right-invariant coframe is different and has the opposite Lie-bracket sign.
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