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

Wolfgang Bertram (1) , Michael Kinyon (2)

1 IECN - Institut Élie Cartan de Nancy
2 University of Denver, Department of Mathematics

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.

Mots clés: classical groups; homotope; associative triple systems; semigroup completion; involution; linear relation; adjoint relation; complemented lattice; orthocomplementation; generalized projection; torsor

Domaines: Anneaux et algèbres [math.RA]

Wolfgang Bertram, Michael Kinyon. Associative Geometries. II: Involutions, the classical torsors, and their homotopes. 2010. ⟨hal-00419639v2⟩