Nonstandard hulls of Banach-Lie groups and algebras

1992/05/19 by Vladimir G. Pestov, Pestov, Vladimir G.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #funct-an #math.OA

paper · pdf · doi:10.48550/arxiv.funct-an/9205003

12 pages

arxiv created 1992/05/19 · arxiv updated 2009/11/30

Abstract

We propose a new construction of Banach-Lie groups and algebras relying on nonstandard analysis. A major standard application is the Local Theorem which to certain extent reduces the problem of associating a Lie group to a given banach-Lie algebra to a similar problem for finitely generated Lie subalgebras. We discuss possible applications, e.g., to gauge theories.

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