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

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

2009-09-24

arxiv.org/abs/0909.4438v2

Mathematics

Rings and Algebras

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

Scientific paper

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.

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