The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, and Alexander Schmeding. "The Lie group of real analytic diffeomorphisms is not real analytic." Studia Mathematica 229.2 (2015): 141-172. <http://eudml.org/doc/285628>.

@article{RafaelDahmen2015,
abstract = { 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. },
author = {Rafael Dahmen, Alexander Schmeding},
journal = {Studia Mathematica},
keywords = {real analytic; manifold of mappings; infinite-dimensional Lie group; regular Lie group; diffeomorphism group; Silva space},
language = {eng},
number = {2},
pages = {141-172},
title = {The Lie group of real analytic diffeomorphisms is not real analytic},
url = {http://eudml.org/doc/285628},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Rafael Dahmen
AU - Alexander Schmeding
TI - The Lie group of real analytic diffeomorphisms is not real analytic
JO - Studia Mathematica
PY - 2015
VL - 229
IS - 2
SP - 141
EP - 172
AB - 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.
LA - eng
KW - real analytic; manifold of mappings; infinite-dimensional Lie group; regular Lie group; diffeomorphism group; Silva space
UR - http://eudml.org/doc/285628
ER -