1Institut Élie Cartan, Université de Nancy, Boulevard des Aiguillettes, B. P. 239, 54506 Vandoeuvre-lès-Nancy, France 2Department of Mathematics, University of Denver, 2360 S Gaylord Street, Denver, CO 80208, U.S.A.
Journal of Lie Theory, Tome 20 (2010) no. 2, pp. 215-252
We define and investigate a geometric object, called an "associative geometry", corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized projective geometries, where the former correspond to the Lie product of an associative algebra and the latter to its Jordan product. A further development of the theory encompassing involutive associative algebras will be given in Part II of this work.
Classification :
20N10, 17C37, 16W10
Mots-clés :
Associative algebras and pairs, torsor, heap, groud, principal homogeneous space, semitorsor, linear relations, homotopy, isotopy, Grassmannian, generalized projective geometry
Affiliations des auteurs :
Wolfgang Bertram
1
;
Michael Kinyon
2
1
Institut Élie Cartan, Université de Nancy, Boulevard des Aiguillettes, B. P. 239, 54506 Vandoeuvre-lès-Nancy, France
2
Department of Mathematics, University of Denver, 2360 S Gaylord Street, Denver, CO 80208, U.S.A.
Wolfgang Bertram; Michael Kinyon. Associative Geometries. I: Torsors, Linear Relations and Grassmannians. Journal of Lie Theory, Tome 20 (2010) no. 2, pp. 215-252. http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a0/
@article{JOLT_2010_20_2_a0,
author = {Wolfgang Bertram and Michael Kinyon},
title = {Associative {Geometries.} {I:} {Torsors,} {Linear} {Relations} and {Grassmannians}},
journal = {Journal of Lie Theory},
pages = {215--252},
year = {2010},
volume = {20},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a0/}
}
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