= Dynamical Lie algebra
{c}
{title2=$\mathfrak g=\operatorname{Lie}_{\mathbb R}\{iH_0,iH_1,\ldots,iH_M\}$}
The dynamical Lie algebra of a finite-dimensional Hamiltonian control system is the real span of its skew-Hermitian drift and control generators and all their nested <commutators>. The sign choice $iH$ or $-iH$ gives the same algebra. Its connected group determines reachable propagators under the usual freely timed, real-control assumptions. An operator commuting with every generator also commutes with this algebra, imposing invariant sectors.
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