Associative Geometries. II: Involutions, the classical torsors, and their homotopes

Abstract

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative geometries. We prove that, under suitable assumptions, the groups and their homotopes have a canonical semigroup completion.

V2: terminology changed ("torsor" instead of "groud"); some improvements in Chapter 3; to appear in Journal of Lie Theory

References in corpus (3)

• Associative Geometries. I: Torsors, linear relations and Grassmannians
• Homotopes and Conformal Deformations of Symmetric Spaces
• Homotopes of Symmetric Spaces II. Structure Variety and Classification

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• Torsors and ternary Moufang loops arising in projective geometry