# 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} }

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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#### References

SHOWING 1-10 OF 29 REFERENCES