Homotopes of Symmetric Spaces
II. Structure Variety and Classification
We classify homotopes of classical symmetric spaces (introduced and
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.
Wolfgang Bertram < Wolfgang.Bertram@iecn.u-nancy.fr >
Pierre Bieliavsky < bieliavsky@math.ucl.ac.be >