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

This is Part II of a work whose first part (revised version) is available as Preprint 271 on the Jordan Server.

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.

(This paper has appeared under the title "Associative Geometries. II: Involutions, the Classical Torsors, and their Homotopes" in Journal of Lie Theory 20 (2) (2010), 253-282)

liejo3.pdf (297K)

W. Bertram < bertram@iecn.u-nancy.fr >

M. Kinyon < mkinyon@math.du.edu >