Homotopes and Conformal Deformations of Symmetric Spaces

Wolfgang Bertram (1)

1 IECN - Institut Élie Cartan de Nancy

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as a special kind of deformation of a given algebraic structure. In this work, we investigate the global counterpart of this phenomenon on the geometric level of the associated symmetric spaces -- on this level, homotopy gives rise to conformal deformations of symmetric spaces. These results are valid in arbitrary dimension and over general base fields and -rings.

Mots clés: homotope; isotope; Jordan algebra (-triple system; -pair); symmetric space; generalized polar and pair geometry

Domaines: Anneaux et algèbres [math.RA]

Wolfgang Bertram. Homotopes and Conformal Deformations of Symmetric Spaces. 2006. ⟨hal-00080542v2⟩