Associative Geometries. I: Torsors, linear relations and Grassmannians

Wolfgang Bertram (1, 2) , Michael Kinyon (1, 2)

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

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 subsequent work.

Mots clés: associative algebras and pairs; torsor (groud; heap; principal homogeneous space); semitorsor; linear relations; homotopy and isotopy; Grassmannian; generalized projective geometry

Domaines: Anneaux et algèbres [math.RA]

Wolfgang Bertram, Michael Kinyon. Associative Geometries. I: Torsors, linear relations and Grassmannians. 2010. ⟨hal-00372160v3⟩