Symmetric bundles and representations of Lie triple systems

Wolfgang Bertram, Manon Didry
2009 Journal of Generalized Lie Theory and Applications  
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
more » ... es on the tangent bundles of certain symmetric spaces.
doi:10.4303/jglta/s090401 fatcat:lk4bxdrd4rah5mnkepabaufe7e