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

Wolfgang Bertram (1) , Pierre Bieliavsky (2)

1 IECN - Institut Élie Cartan de Nancy
2 UCL IRMP - Institut de Recherche en Mathématiques et Physique

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''.

Mots clés: contraction; associative algebra; involution; homotope (isotope); Lie algebra; Lie triple system; extrinsic symmetric space; symmetric space

Domaines: Géométrie différentielle [math.DG]

Wolfgang Bertram, Pierre Bieliavsky. Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions. 2012. ⟨hal-00535693v2⟩