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Licensed Unlicensed Requires Authentication Published by De Gruyter July 11, 2013

A local-to-global result for topological spherical buildings

  • Rupert McCallum EMAIL logo
From the journal Advances in Geometry

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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