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. A symmetric 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.
@article{1281106595,
author = {Bertram, Wolfgang and Didry, Manon},
title = {Symmetric bundles and representations of Lie triple systems},
journal = {J. Gen. Lie Theory Appl.},
volume = {3},
number = {3},
year = {2009},
pages = { 261-284},
language = {en},
url = {http://dml.mathdoc.fr/item/1281106595}
}
Bertram, Wolfgang; Didry, Manon. Symmetric bundles and representations of Lie triple systems. J. Gen. Lie Theory Appl., Tome 3 (2009) no. 3, pp. 261-284. http://gdmltest.u-ga.fr/item/1281106595/