Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
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Publication:1865306
DOI10.1006/jfan.2002.3942zbMath1022.22021OpenAlexW1963863391MaRDI QIDQ1865306
Publication date: 26 March 2003
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jfan.2002.3942
exponential functionBaker-Campbell-Hausdorff formulacomplexificationBanach Lie groupsinfinite-dimensional Lie groupBaker-Campbell-Hausdorff (BCH) Lie groupsdirect limit groupsmapping groups
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Cites Work
- Differentiable structure for direct limit groups
- Differential calculus in locally convex spaces
- On group topologies and unitary representations of inductive limits of topological groups and the case of the group of diffeomorphisms
- A Cartan-Hadamard theorem for Banach-Finsler manifolds
- Central extensions of infinite-dimensional Lie groups
- Direct limit Lie groups and manifolds
- Espaces fibres en algèbres de Lie et en groupes
- Applications différentiables et variétés différentiables de dimension infinie
- Lie groups with Banach spaces as parameter spaces
- The Bott–Borel–Weil Theorem for direct limit groups
- Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
- The inverse function theorem of Nash and Moser
- Polar and Ol'shanskii decompositions.
- Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
- Banach-Lie quotients, enlargibility, and universal complexifications
- A quick proof of the classification of simple real Lie algebras
- On Sequential Convergence
- Complexification of Real Analytic Groups
- Polynomials and multilinear mappings in topological vector-spaces
- Analytic functions in topological vector-spaces
- Some Theorems on Direct Limits of Expanding Sequences of Manifolds.
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