nLab
infinite-dimensional Lie group

Idea

A group object in infinite-dimensional smooth manifolds is an infinite-dimensional Lie group.

If the underlying type of manifolds is Banach manifold, then one speaks of Banach-Lie groups, etc.

Examples

• stable unitary group

• loop group

• diffeomorphism group

  • symplectomorphism group, quantomorphism group

• Butcher group

References

• Andreas Kriegl, Peter Michor, Regular infinite dimensional Lie groups Journal of Lie Theory

  Volume 7 (1997) 61-99 (pdf)

• Rudolf Schmid, Infinite-Dimensional Lie Groups and Algebras in Mathematical Physics Advances in Mathematical Physics Volume 2010, (pdf)

• Josef Teichmann, Innite dimensional Lie Theory from the point of view of Functional Analysis (pdf)

• Karl-Hermann Neeb, Monastir summer school: Infinite-dimensional Lie groups (pdf)

• Karl-Hermann Neeb, Towards a Lie theory of locally convex groups (pdf)