Associative Geometries. II: Involutions, the classical grouds, 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 {\em homotopes}. The construction is geometric, using as ingredient {\em involutions of associative geometries}. We prove that, under suitable assumptions, the groups and their homotopes have a canonical semigroup completion.

Mots clés: Lie-Jordan algebras; Jordan-Lie algebras; Hermitian projective line; classical groups; associative triple systems; ternary rings of operators; groud; semigroud

Domaines: Anneaux et algèbres [math.RA]

Wolfgang Bertram, Michael Kinyon. Associative Geometries. II: Involutions, the classical grouds, and their homotopes. 2009. ⟨hal-00419639v1⟩