Open Access
December 2009 Symmetric bundles and representations of Lie triple systems
Wolfgang Bertram, Manon Didry
J. Gen. Lie Theory Appl. 3(4): 261-284 (December 2009). DOI: 10.4303/jglta/S090401


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.


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Wolfgang Bertram. Manon Didry. "Symmetric bundles and representations of Lie triple systems." J. Gen. Lie Theory Appl. 3 (4) 261 - 284, December 2009.


Published: December 2009
First available in Project Euclid: 6 August 2010

zbMATH: 1239.17001
MathSciNet: MR2602990
Digital Object Identifier: 10.4303/jglta/S090401

Primary: 17A01 , 17B10
Secondary: 53C35

Keywords: algebraic theory , Differential geometry , Lie algebras representations , Lie superalgebras representations , Nonassociative rings and algebras , symmetric spaces

Rights: Copyright © 2009 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • No. 4 • December 2009
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