Symmetric bundles and representations of Lie triple systems
Abstract
We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. We show that such a bundle has an underlying reflection space, and we investigate the corresponding forgetful functor both from the point of view of differential geometry and from the point of view of representation theory. This functor is not injective, as is seen by constructing "unusual" symmetric bundle structures on the tangent bundles of certain symmetric spaces.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1543
 Bibcode:
 2007arXiv0710.1543B
 Keywords:

 Mathematics  Differential Geometry;
 17A01;
 17B10;
 53C15
 EPrint:
 22 pages, v2: minor corrections