Petra Hitzelberger

Base change of generalized affine buildings

Group actions on \Lambda-trees have been studied by Alperin, Bass, Morgan,
Shalen and others and have proven to be a useful tool in understanding
properties of groups. Here \Lambda can be any ordered abelian group.
                                                                          
The \Lambda-trees are a natural generalization of R-trees.
Since simplicial trees are precisely the one-dimensional examples of affine
buildings and real trees the one-dimensional ones in the class of R-buildings
it is natural to ask, whether there is a higher dimensional object
generalizing \Lambda-trees and affine buildnigs at the same time.
                                                  
These objects exists, they are the so called affine \Lambda- buildings (or 
generalized affine buildings). In my talk I will introduce these spaces and  
discuss some of its geometric properties.                                    
                                                                              
I will explain how a morphism e:\Lambda \to\Gamma of ordered abelian groups   
gives rise to a base change functor mapping a generalized affine building    
defined over \Lambda to another defined over \Gamma.                         
                                                                              
As a consequence of the base change theorem one obtains a graph of groups     
decomposition for groups acting nicely on generalized affine buildings which 
are defined over Z\times\Lambda.