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 >