Construction of the cotangent bjundle of a locally compact group

摘要

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 symplecfcic form w 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).