Nonstandard Hulls of Locally Exponential Lie Algebras

2008/04/03 by Isaac Goldbring, Goldbring, Isaac
Mathematics · #22E65 #26E35 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical and Theoretical Analysis #math.DG #math.LO #msc:22E65 #msc:26E35

paper · pdf · doi:10.48550/arxiv.0804.0565

arxiv created 2008/04/03 · openalex publication_date 2008/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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