The Lie group of real analytic diffeomorphisms is not real analytic

• Autorzy: Rafael Dahmen , Alexander Schmeding
• Języki publikacji: EN

Abstrakty

EN

We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor.
In the inequivalent "convenient setting of calculus" the real analytic diffeomorphisms even form a real analytic Lie group. However, we prove that the Lie group structure on the group of real analytic diffeomorphisms is in general not real analytic in our sense.

Kategorie tematyczne

• 26E05: Real-analytic functions
• 58B10: Differentiability questions
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties
• 58D15: Manifolds of mappings
• 58D05: Groups of diffeomorphisms and homeomorphisms as manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 229
• Numer: 2
• Strony: 141-172

Daty

wydano

2015

Twórcy

autor

Rafael Dahmen

• Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany

autor

Alexander Schmeding

• Institutt for matematiske fag, NTNU Trondheim, 7032 Trondheim, Norway

Identyfikatory

DOI

10.4064/sm8130-12-2015