Towards a Lie theory of locally convex groups
By Karl-Hermann Neeb. 2006
304 citations recorded by the source corpus.
Abstract.In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie subgroups, and integrability of Lie algebra extensions to Lie group extensions. We further describe how regularity or local exponentiality of a Lie group can be used to obtain quite satisfactory answers to some of the fundamental problems. These results are illustrated by specialization to some specific classes of Lie groups, such as direct limit groups, linear Lie groups, groups of smooth maps and groups of diffeomorphisms.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/29799925fed953f1dafd6cda8d233c8e22d1362f
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In Algebra and Number Theory
- Hamza Alzaareer
- Thomas Schulte-Herbrüggen
- Ronnie Kosloff
- Dominique Sugny
- Alexander Schmeding
- Tommaso Calarco
- Christiane P. Koch
- Frank K. Wilhelm
In Mathematical Physics
Citations in the corpus
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, methodology): “At the level of methods, extending finite-dimensional Lie-group and Liesemigroup techniques to infinite dimensions [435] is a challenging desideratum.”
- Differentiable mappings on products with different degrees of differentiability in the two factors (2012, background): “Many results in infinite-dimensional Lie theory are only available for regular Lie groups (see [31], [23], [33], [36] and the references therein, cf.”