Regularity and completeness of halfLie groups
Abstract
Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely required to be continuous. The main examples are groups of $H^s$ or $C^k$ diffeomorphisms and semidirect products of a Lie group with kernel an infinite dimensional representation space. Here, we investigate mainly Banach halfLie groups, the groups of their $C^k$elements, extensions, and right invariant strong Riemannian metrics on them: surprisingly the full HopfRinow theorem holds, which is wrong in general even for Hilbert manifolds.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.01631
 arXiv:
 arXiv:2302.01631
 Bibcode:
 2023arXiv230201631B
 Keywords:

 Mathematics  Differential Geometry;
 58B25;
 58D05;
 58B20
 EPrint:
 41 pages