Weighted diffeomorphism groups of Banach spaces and weighted mapping groups

Boris Walter. Weighted diffeomorphism groups of Banach spaces and weighted mapping groups. 2012. <http://eudml.org/doc/286041>.

@book{BorisWalter2012,
abstract = {In this work, we construct and study certain classes of infinite-dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group $Diff_\{\}(X)$ of diffeomorphisms, for each Banach space X and each set of weights on X containing the constant weights. We also construct certain types of “weighted mapping groups”. These are Lie groups modelled on weighted function spaces of the form $_\{\}^\{k\}(U,L(G))$, where G is a given (finite- or infinite-dimensional) Lie group. Both the weighted diffeomorphism groups and the weighted mapping groups are shown to be regular Lie groups in Milnor’s sense. We also discuss semidirect products of such groups. Moreover, we study the integrability of Lie algebras of vector fields of the form $_\{\}^\{∞\}(X,X) ⋊ L(G)$, where X is a Banach space and G a Lie group acting smoothly on X.},
author = {Boris Walter},
keywords = {infinite-dimensional Lie group; diffeomorphism group; mapping group; gauge group; current group; noncompact manifold; weighted function space; rapidly decreasing function; Schwartz space; semidirect product; Banach manifold},
language = {eng},
title = {Weighted diffeomorphism groups of Banach spaces and weighted mapping groups},
url = {http://eudml.org/doc/286041},
year = {2012},
}

TY - BOOK
AU - Boris Walter
TI - Weighted diffeomorphism groups of Banach spaces and weighted mapping groups
PY - 2012
AB - In this work, we construct and study certain classes of infinite-dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group $Diff_{}(X)$ of diffeomorphisms, for each Banach space X and each set of weights on X containing the constant weights. We also construct certain types of “weighted mapping groups”. These are Lie groups modelled on weighted function spaces of the form $_{}^{k}(U,L(G))$, where G is a given (finite- or infinite-dimensional) Lie group. Both the weighted diffeomorphism groups and the weighted mapping groups are shown to be regular Lie groups in Milnor’s sense. We also discuss semidirect products of such groups. Moreover, we study the integrability of Lie algebras of vector fields of the form $_{}^{∞}(X,X) ⋊ L(G)$, where X is a Banach space and G a Lie group acting smoothly on X.
LA - eng
KW - infinite-dimensional Lie group; diffeomorphism group; mapping group; gauge group; current group; noncompact manifold; weighted function space; rapidly decreasing function; Schwartz space; semidirect product; Banach manifold
UR - http://eudml.org/doc/286041
ER -