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Journal of Lie Theory 18 (2008), No. 2, 301--333
Copyright Heldermann Verlag 2008

Homotopes and Conformal Deformations of Symmetric Spaces

Wolfgang Bertram
Institut Elie Cartan, Dép. de Mathématiques, Université Henri Poincaré, B.P. 239, 54506 Vandoeuvres-Les-Nancy, France

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among each 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 geometric counterpart of this phenomenon on the 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.

Keywords: Homotope, isotope, Jordan algebras, Jordan triple systems, Jordan pairs, Lie triple system, symmetric space, generalized projective geometries, polar geometries.

MSC: 17C37, 32G99, 17C27, 14D99

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