nLab
infinite-dimensional Lie group

Contents

Context

Group Theory

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

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

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)

Last revised on August 23, 2018 at 03:40:06. See the history of this page for a list of all contributions to it.