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 $A'(G)$. 
@article{IM2_1995_59_3_a0,
     author = {S. S. Akbarov},
     title = {Construction of the cotangent bundle of a~locally compact group},
     journal = {Izvestiya. Mathematics },
     pages = {445--470},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a0/}
}
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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/