Construction of the cotangent bundle of a locally compact group

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 $A'(G)$.