Geodesic
Construction of the cotangent bundle of a locally compact group
Izvestiya. Mathematics, Tome 59 (1995) no. 3, pp. 445-470 
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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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $A'(G)$.

[1] Bruhat F., “Distributions sur un groupe localement compact et applications a l'etude des representations des groupes $p$-adiques”, B. Soc. Math. France, 89:1 (1961), 43–75 | MR | Zbl

[2] Akbarov S. S., “Gladkaya struktura i differentsialnye operatory na lokalno kompaktnoi gruppe”, Izv. AN. Ser. matem., 59:1 (1995), 3–48 | MR | Zbl

[3] Akbarov S. S., “Differentsialnaya geometriya i kvantovanie na lokalno kompaktnoi gruppe”, Izv. AN. Ser. matem., 59:2 (1995), 47–96 | MR

[4] Vinogradov A. M., Krasilschik I. S., “Chto takoe gamiltonov formalizm?”, UMN, 30:1(181) (1975), 172–198

[5] Kakutani S., Klee V., “The finite topology of a linear space”, Arch. Math., 14:1 (1963), 55–58 | DOI | MR | Zbl

[6] Kelli Dzh. L., Obschaya topologiya, Nauka, M., 1981 | MR

[7] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966 | MR

[8] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[9] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[10] Kirillov A. A., Vvedenie v teoriyu predstavlenii i nekommutativnyi garmonicheskii analiz, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 22, VINITI, M., 1988 | MR