Fundamentals of direct limit Lie theory

2005/11/01 by Helge Glöckner · 6 citations
Mathematics · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.1112/s0010437x05001491

Abstract

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).

Citations

• Principal series representations of direct limit groups

Cited by

• Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions
• On differentiability of vectors in Lie group representations
• Smooth Homotopy of Infinite-Dimensional C^∞-Manifolds
• Concentration of measure for classical Lie groups
• Differentiable vectors and unitary representations of Frechet-Lie\n supergroups
• Integrating central extensions of Lie algebras via Lie 2-groups

Related

• Fundamentals of direct limit Lie theory
• Direct limits of regular Lie groups
• Direct limit groups do not have small subgroups
• Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories
• Direct limits of infinite-dimensional Lie groups