Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions

Details Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions

2010-11-12

arxiv.org/abs/1011.2923v2

Mathematics

Differential Geometry

V2: minor corrections

Scientific paper

We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an elementary way by using associative algebras with several involutions. This construction shows a remarkable duality between the underlying "space" and the "deformation parameter".

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