Generalized projective geometries: general theory and equivalence with Jordan structures

DOI10.1515/advg.2002.016zbMath1035.17043OpenAlexW4248978216MaRDI QIDQ4785509

Wolfgang Bertram

Publication date: 2 January 2003

Published in: advg (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/123433

zbMATH Keywords

symmetric spaceprojective geometryJordan pairpolar geometryJordan triple systemgeneralized projective geometryJordan functorprojective geometries over rings

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70) Differential geometry of symmetric spaces (53C35) General theory of linear incidence geometry and projective geometries (51A05) Polar geometry, symplectic spaces, orthogonal spaces (51A50) Associated groups, automorphisms of Jordan algebras (17C30) Associated manifolds of Jordan algebras (17C36) Associated geometries of Jordan algebras (17C37)

Related Items (11)

Projective completions of Jordan pairs. I: The generalized projective geometry of a Lie algebra ⋮ The \textit{XJC}-correspondence ⋮ Possible primitive notions for geometry of spine spaces ⋮ Inner ideals and intrinsic subspaces of linear pair geometries ⋮ Jordan Structures and Non-Associative Geometry ⋮ Is there a Jordan geometry underlying quantum physics? ⋮ C-projective geometry ⋮ From linear algebra via affine algebra to projective algebra ⋮ Differential calculus over general base fields and rings. ⋮ Projective completions of Jordan pairs. II: Manifold structures and symmetric spaces ⋮ The geometry of null systems, Jordan algebras and von Staudt's theorem.

Cites Work

• The geometry of Jordan and Lie structures
• On an algebraic generalization of the quantum mechanical formalism
• Elementary groups and stability for Jordan pairs
• Unnamed Item

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