Fundamentals of direct limit Lie theory
By Helge Glöckner. Compositio Mathematica, 2004
48 citations recorded by the source corpus.
We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push all basic constructions of finite-dimensional Lie theory to the case of direct limit groups. In particular, we obtain an analogue of Lie's third theorem: every countable-dimensional locally finite real or complex Lie algebra arises as the Lie algebra of some regular Lie group (a suitable direct limit group).
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6a50082878819fbdbd62f6cbd5cb8ac902aa5fd5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Ralf Gramlich
- Tobias Hartnick
- Helge Glöckner
- Karl-Hermann Neeb
- W. Bertram
- Hamza Alzaareer
- Alexander Schmeding
In Mathematical Physics
- Ralf Gramlich
- Tobias Hartnick
- Helge Glöckner
- Karl-Hermann Neeb
- Hamza Alzaareer
- Alexander Schmeding
- W. Bertram
Citations in the corpus
- Final group topologies, Kac-Moody groups and Pontryagin duality (2006, background): “2 Among the main examples of infinite-dimensional Lie groups are direct limits G = lim −→ Gn of ascending sequences G1 ⊆ G2 ⊆ · · · of finite-dimensional Lie groups, such that the inclusion maps are continuous homomorphisms (see [27], [28], [70]).”