Pro-Lie groups which are infinite-dimensional Lie groups

@article{Hofmann2009ProLieGW,
  title={Pro-Lie groups which are infinite-dimensional Lie groups},
  author={K. Hofmann and K. Neeb},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2009},
  volume={146},
  pages={351 - 378}
}
  • K. Hofmann, K. Neeb
  • Published 2009
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
Abstract A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this paper we show that a pro-Lie group G is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if G is locally contractible. We also characterize the corresponding pro-Lie algebras in various ways. Furthermore, we characterize those pro-Lie groups which are locally exponential, that is, they are Lie groups… Expand
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