The paper identifies the Toda symmetry algebra with a central extension of the stochastic Lie algebra, but the claimed Lie-Bianchi integrability on the full phase space is not established.
Arhangelskii, Completely integrable hamiltonian systems on a group of triangular matrices, Mathematics of the USSR-Sbornik, 36:1, 127–134 (1980)
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The Lie -Bianchi integrability of the full symmetric Toda system
The paper identifies the Toda symmetry algebra with a central extension of the stochastic Lie algebra, but the claimed Lie-Bianchi integrability on the full phase space is not established.