Homotopes of Symmetric Spaces II. Structure Variety and Classification

Wolfgang Bertram (1) , Pierre Bieliavsky (2)

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

We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base spaces correspond to inner ideals in Jordan pairs. Using that inner ideals in classical Jordan pairs are always complemented (in the sense defined by O. Loos and E. Neher), the classification of homotopes is obtained by combining the classification of inner ideals with the one of isotopes of a given inner ideal.

Mots clés: involution; inner ideal; symmetric space; pseudo-inverse; idempotent; 3-graded Lie algebra; Jordan pairs and triple systems; homotope (isotope); structural transformation; Lie triple system; contraction; complementation

Domaines: Géométrie différentielle [math.DG]

Wolfgang Bertram, Pierre Bieliavsky. Homotopes of Symmetric Spaces II. Structure Variety and Classification. 2012. ⟨hal-00535877v2⟩