Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions

Abstract

We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an elementary way by using associative algebras with several involutions. This construction shows a remarkable duality between the underlying "space" and the "deformation parameter".

V2: minor corrections

References in corpus (4)

• The deformation quantizations of the hyperbolic plane
• Associative Geometries. I: Torsors, linear relations and Grassmannians
• Homotopes and Conformal Deformations of Symmetric Spaces
• Homotopes of Symmetric Spaces II. Structure Variety and Classification

Cited by in corpus (1)

• Homotopes of Symmetric Spaces II. Structure Variety and Classification