Inclusions of invariant subalgebras S(g)^G subset S(g)^T subset S(g) for a maximal torus T in a semisimple Lie group G form a superintegrable Poisson projection chain with matching dimension splits between Hamiltonians and integrals.
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Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Inclusions of invariant subalgebras S(g)^G subset S(g)^T subset S(g) for a maximal torus T in a semisimple Lie group G form a superintegrable Poisson projection chain with matching dimension splits between Hamiltonians and integrals.