Inner ideals and intrinsic subspaces of linear pair geometries
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Abstract
We introduce the notion of intrinsic subspaces of linear and affine pair geometries, which generalizes the one of projective subspaces of projective spaces. We prove that, when the affine pair geometry is the projective geometry of a Lie algebra introduced in [W. Bertram, K.-H. Neeb, Projective completions of Jordan pairs. I. The generalized projective geometry of a Lie algebra. J. Algebra277 (2004), 474–519. MR2067615 (2005f:17031) Zbl 02105235], such intrinsic subspaces correspond to inner ideals in the associated Jordan pair, and we investigate the case of intrinsic subspaces defined by the Peirce-decomposition which is related to 5-gradings of the projective Lie algebra. These examples, as well as the examples of general and Lagrangian flag geometries, lead to the conjecture that geometries of intrinsic subspaces tend to be themselves linear pair geometries.
© de Gruyter 2008
Articles in the same Issue
- Ruled Weingarten hypersurfaces in
- Constructing topological parallelisms of PG(3, ℝ) via rotation of generalized line pencils
- A Gauss–Bonnet formula for closed semi-algebraic sets
- Inner ideals and intrinsic subspaces of linear pair geometries
- Staircase kernels
- Twisted McFarland and Spence designs and their automorphisms
- On the relative lengths of the sides of convex polygons
- The structure of full polarized embeddings of symplectic and Hermitian dual polar spaces
- Polar spaces, BLT-sets and generalized quadrangles
- Erratum to “On the Hilbert scheme of Palatini threefolds”
Articles in the same Issue
- Ruled Weingarten hypersurfaces in
- Constructing topological parallelisms of PG(3, ℝ) via rotation of generalized line pencils
- A Gauss–Bonnet formula for closed semi-algebraic sets
- Inner ideals and intrinsic subspaces of linear pair geometries
- Staircase kernels
- Twisted McFarland and Spence designs and their automorphisms
- On the relative lengths of the sides of convex polygons
- The structure of full polarized embeddings of symplectic and Hermitian dual polar spaces
- Polar spaces, BLT-sets and generalized quadrangles
- Erratum to “On the Hilbert scheme of Palatini threefolds”
