Geodesic
Associative Geometries. II: Involutions, the Classical Torsors, and their Homotopes
Journal of Lie theory, Tome 20 (2010) no. 2, pp. 253-282 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 20N10, 17C37, 16W10
Mots-clés : Classical groups, homotope, associative triple systems, semigroup completion, involution, linear relation, adjoint relation, complemented lattice, orthocomplementation, generalized projection, torsor 
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     author = {W. Bertram and M. Kinyon },
     title = {Associative {Geometries.} {II:} {Involutions,} the {Classical} {Torsors,} and their {Homotopes}},
     journal = {Journal of Lie theory},
     pages = {253--282},
     year = {2010},
     volume = {20},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a1/}
}
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W. Bertram; M. Kinyon . Associative Geometries. II: Involutions, the Classical Torsors, and their Homotopes. Journal of Lie theory, Tome 20 (2010) no. 2, pp. 253-282. http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a1/