Associative Geometries. I: Grouds, Linear Relations and Grassmannians
نویسندگان
چکیده
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 [BeKi09].
منابع مشابه
. R A ] 2 4 Se p 20 09 ASSOCIATIVE GEOMETRIES . II : INVOLUTIONS , THE CLASSICAL GROUDS , AND THEIR HOMOTOPES
For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called homotopes. The construction is geometric, using as ingredient involutions of associative geometries. We prove that, under suitable assumptions, the groups and their homotopes have a canonical semigroup completion. Introduction: The classical group...
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