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Homotopes and conformal deformations of symmetric spaces. (English) Zbl 1164.17021

As it is well-known, 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 the present paper, the author investigates 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.

MSC:

17C37 Associated geometries of Jordan algebras
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
17C36 Associated manifolds of Jordan algebras
53C35 Differential geometry of symmetric spaces
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