Geometry over composition algebras : projective geometry

Details Geometry over composition algebras : projective geometry Geometry over composition algebras : projective geometry

2005-09-23

arxiv.org/abs/math/0509549v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in correspondance with Jordan algebras and that the points of a projective space correspond to rank one matrices in the Jordan algebra. A second part thus studies properties of rank one matrices. Finally, subvarieties of projective spaces are discussed.

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