Differentiable structure for direct limit groups

DOI10.1007/BF00703721zbMath0762.22017MaRDI QIDQ1182293

Enriqueta Rodríguez-Carrington, Loki Natarajan, Joseph A. Wolf

Publication date: 28 June 1992

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

exponential mapdiscrete spectrumdifferentiable structuredirect limit of Lie algebrasdirect limit of Lie groupsspectral growth condition

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Limits, profinite groups (20E18) Associated Lie structures for groups (20F40)

Related Items (12)

Direct limit groups do not have small subgroups ⋮ Completeness of locally \(k_{\omega}\)-groups and related infinite-dimensional Lie groups ⋮ Conical representations for direct limits of symmetric spaces ⋮ Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories ⋮ Final group topologies, Kac-Moody groups and Pontryagin duality ⋮ Completeness of Infinite-dimensional Lie Groups in Their Left Uniformity ⋮ Solutions to open problems in Neeb's recent survey on infinite-dimensional Lie groups ⋮ The Bott–Borel–Weil Theorem for direct limit groups ⋮ Towards a Lie theory of locally convex groups ⋮ Differential calculus over general base fields and rings. ⋮ Hilbert--Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry ⋮ Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups

Cites Work

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• A simple independent-particle system having collective properties
• Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space
• Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
• Unitary representations of maximal parabolic subgroups of the classical groups

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