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

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”.