2005/09/23 by Pierre-Emmanuel Chaput, Chaput, Pierre-Emmanuel
Mathematics · #14L35 #14L40 #14N99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L35 #msc:14L40 #msc:14N99
paper · pdf · doi:10.48550/arxiv.math/0509549
24 pages
arxiv created 2005/09/23 · arxiv updated 2009/12/01
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.