Achtung:

Sie haben Javascript deaktiviert!
Sie haben versucht eine Funktion zu nutzen, die nur mit Javascript möglich ist. Um sämtliche Funktionalitäten unserer Internetseite zu nutzen, aktivieren Sie bitte Javascript in Ihrem Browser.

Bildinformationen anzeigen

Nonstandard Hulls of Locally Exponential Lie Groups and Algebras

Isaac Goldbring

Abstract

In the early 90s, V. Pestov used nonstandard analysis to prove the following theorem on the enlargeability of Banach-Lie algebras: Suppose g is a Banach-Lie algebra which has a directed family {h_i} of enlargeable subalgebras whose union is dense in g. Further suppose there is a single neighborhood V of 0 in g for which the exponential map of each h_i restricted to V is injective. Then g is enlargeable. The key nonstandard idea in Pestov's proof is the nonstandard hull construction. I will explain how to generalize this construction to the wider class of locally exponential Lie groups and algebras satisfying certain extra assumptions, yielding a partial generalization of Pestov's theorem. I will assume no familiarity with nonstandard methods and will introduce all necessary nonstandard material.

Die Universität der Informationsgesellschaft