Homotopes of Symmetric Spaces II. Structure Variety and Classification

Details Homotopes of Symmetric Spaces II. Structure Variety and Classification Homotopes of Symmetric Spaces II. Structure Variety and Classification

2010-11-13

arxiv.org/abs/1011.3161v2

Mathematics

Differential Geometry

V2: minor corrections and modifications

Scientific paper

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.

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