2010/05/18 by Wolfgang Bertram, Michael Kinyon, Bertram, Wolfgang +1
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1005.3192
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
arxiv created 2010/05/18 · arxiv updated 2010/05/19
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.