Associative Geometries. I: Torsors, linear relations and GrassmanniansReport as inadecuate




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1 IECN - Institut Élie Cartan de Nancy 2 University of Denver, Department of Mathematics

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.

Keywords : associative algebras and pairs torsor groud heap principal homogeneous space semitorsor linear relations homotopy and isotopy Grassmannian generalized projective geometry





Author: Wolfgang Bertram - Michael Kinyon -

Source: https://hal.archives-ouvertes.fr/



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