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A local-to-global result for topological spherical buildings
Published/Copyright:
July 11, 2013
Abstract
Suppose that Δ;Δʹ are two buildings each arising from a semisimple algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter diagram has no isolated nodes. We give conditions under which a partially defined injective chamber map, whose domain is the subcomplex of Δ generated by a nonempty open set of chambers, and whose codomain is Δʹ, is guaranteed to extend to a unique injective chamber map. Related to this result is a local version of the Borel-Tits theorem on abstract homomorphisms of simple algebraic groups.
Published Online: 2013-07-11
Published in Print: 2013-07
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Index and nullity of a family of harmonic tori in the sphere
- G-Fano threefolds, I
- G-Fano threefolds, II
- A local-to-global result for topological spherical buildings
- Biaffine polar spaces
- Adjoint pluricanonical systems on varieties of general type
- Hypersurfaces of revolution with proportional principal curvatures
- On metrically complete Bruhat–Tits buildings
- Veroneseans, power subspaces and independence
- Baer involutions and polarities in Moufang planes of characteristic two
- The Chern invariants for parabolic bundles at multiple points
Keywords for this article
Topological geometry;
local homomorphism;
topological building;
Borel-Tits theorem
Articles in the same Issue
- Masthead
- Index and nullity of a family of harmonic tori in the sphere
- G-Fano threefolds, I
- G-Fano threefolds, II
- A local-to-global result for topological spherical buildings
- Biaffine polar spaces
- Adjoint pluricanonical systems on varieties of general type
- Hypersurfaces of revolution with proportional principal curvatures
- On metrically complete Bruhat–Tits buildings
- Veroneseans, power subspaces and independence
- Baer involutions and polarities in Moufang planes of characteristic two
- The Chern invariants for parabolic bundles at multiple points
