Homotopes and Conformal Deformations of Symmetric Spaces

Abstract

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.

arXiv comment28 pages, 2nd corrected version

Cited by in corpus (5)

• Associative Geometries. I: Torsors, linear relations and Grassmannians
• Associative Geometries. II: Involutions, the classical torsors, and their homotopes
• The projective geometry of a group
• Homotopes of Symmetric Spaces II. Structure Variety and Classification
• Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions