Geodesic
Construction of the cotangent bundle of a~locally compact group
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 445-470.

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The existence is proved of “a generalized” smooth structure on the cotangent bundle $T'G$ of an arbitrary locally compact group $G$, turning $T'G$ into a paracompact (possibly infinite-dimensional) smooth manifold. A symplectic form $\omega$ on $T'G$ is constructed, which is naturally related to the Poisson brackets in the algebra of symbols on $G$ and the Lie–Poisson structure in the momentum space $A'(G)$. 
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S. S. Akbarov. Construction of the cotangent bundle of a~locally compact group. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 445-470. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a0/

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