Associative Geometries. I: Torsors, linear relations and Grassmannians

Details Associative Geometries. I: Torsors, linear relations and Grassmannians Associative Geometries. I: Torsors, linear relations and Grassmannians

2010-05-18

arxiv.org/abs/1005.3192v1

Mathematics

Rings and Algebras

v2: new results on relation with lattice theory added (Th. 2.4) v3: title and terminology changed: "torsor" instead of "groud"

Scientific paper

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.

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