Symmetric bundles and representations of Lie triple systems

Details Symmetric bundles and representations of Lie triple systems Symmetric bundles and representations of Lie triple systems

2007-10-08

arxiv.org/abs/0710.1543v2

Mathematics

Differential Geometry

22 pages, v2: minor corrections

Scientific paper

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.

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