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1 results

  • Fundamentals of direct limit Lie theory

  • Helge Glöckner
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 6 / November 2005
    Published online by Cambridge University Press:
    04 December 2007, pp. 1551-1577
    Print publication:
    November 2005
    • Article
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  • 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).