Associative Geometries. I: Torsors, linear relations and Grassmannians
Rings and Algebras
2010-05-31 v3
Abstract
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.
Cite
@article{arxiv.0903.5441,
title = {Associative Geometries. I: Torsors, linear relations and Grassmannians},
author = {Wolfgang Bertram and Michael Kinyon},
journal= {arXiv preprint arXiv:0903.5441},
year = {2010}
}
Comments
v2: new results on relation with lattice theory added (Th. 2.4) v3: title and terminology changed: "torsor" instead of "groud"; to appear in Journal of Lie Theory