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''.

Wolfgang Bertram < Wolfgang.Bertram@iecn.u-nancy.fr >

Pierre Bieliavsky < bieliavsky@math.ucl.ac.be >