Nonstandard Hulls of Locally Exponential Lie Algebras

Details Nonstandard Hulls of Locally Exponential Lie Algebras Nonstandard Hulls of Locally Exponential Lie Algebras

2008-04-03

arxiv.org/abs/0804.0565v1

Mathematics

Differential Geometry

Scientific paper

We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced function between the nonstandard hulls is smooth. We also discuss some conditions on a function between locally convex spaces which guarantee that its nonstandard extension maps finite points to finite points.

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