Abstract
The symplectic two-cocycle on the semidirect product Lie algebra g⨷(W⊕V*⊕V) is shown to be canonically related to the dual spaces of the Lie algebras (a) g⨷(W⊕(g⨷V)) and (b) g⨷(W⊕(g⨷V*)). This fact (a) explains the second Poisson bracket for irrotational 4He and (b) leads to a derivation of a new nonlinear Poisson bracket for rotating 4He.
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