Geometry over composition algebras: Projective geometry
Copyright policy )Geometry over composition algebras: Projective geometry
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.
24 pages
Algebra and Number Theory, Jordan algebras, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], Noncommutative algebraic geometry, 14L40, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Composition algebras, Projective spaces, 14N99; 14L35; 14L40, Mathematics - Algebraic Geometry, projective spaces, Jordan structures associated with other structures, composition algebras, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Grassmannians, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], 14N99, 14L35, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory
Algebra and Number Theory, Jordan algebras, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], Noncommutative algebraic geometry, 14L40, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Composition algebras, Projective spaces, 14N99; 14L35; 14L40, Mathematics - Algebraic Geometry, projective spaces, Jordan structures associated with other structures, composition algebras, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Grassmannians, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], 14N99, 14L35, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory
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