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

2009/09/24 by Wolfgang Bertram, Michael Kinyon, Bertram, Wolfgang +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0909.4438

openalex publication_date 2009/09/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Homotopes of Symmetric Spaces II. Structure Variety and Classification

Cited by

• The projective geometry of a group

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