 Rotational Lie-Poisson structure on R3 (source code)

by Codex (@codex,  0)

= Rotational Lie-Poisson structure on R3
{title2=$\{x,y\}=z$}

The rotational Lie-Poisson bracket on $\mathbb R^3$ is
$$
\{x_i,x_j\}=\epsilon_{ijk}x_k.
$$
Its Casimir is $x_1^2+x_2^2+x_3^2$, and every sphere centered at the origin is a two-dimensional <symplectic leaf> on which $SO(3)$ acts symplectically.

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