Remark

Let H be a connected real or complex Lie group, \tilde{H} its universal covering† and \pi the canonical mapping of \tilde{H} onto H. When we speak of \tilde{H}

† Cf. General Topology, Chapter XI; whilst awaiting the publication of this chapter, see for example L. S. Pontrjagin, Topological groups, 2nd edition translated from Russian, Gordon and Breach, 1966; or G. Hochschild, The structure of Lie groups, Holden-Day, 1965.

LIE GROUPS

as a Lie group, we shall always mean with the inverse image structure of that on H under $\pi$.