Associative Geometries. I: Grouds, linear relations and Grassmannians
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.
(This paper has appeared under the title "Associative Geometries. I:
Torsors, Linear Relations and Grassmannians" in Journal of Lie Theory 20 (2)
(2010), 215-252)
W. Bertram < bertram@iecn.u-nancy.fr >
M. Kinyon < mkinyon@math.du.edu >