A smooth structure on a locally compact topological group

Tomasz Rybicki University of Mining and Metallurgy, Cracow

It is shown that any connected locally compact topological group (or, more generally, any PL-group) carries a smooth structure. Here a smooth structure is determined by a set of smooth curves with some conditions specified. It is observed that the Lie algebra of a locally compact group is identified with the Lie algebra assigned to a smooth group structure. Further properties are exhibited.