Journal of Geometry

, 110:18 | Cite as

A structure theorem for euclidean buildings

  • Petra SchwerEmail author
  • David Weniger


We prove an affine analog of Scharlau’s reduction theorem for spherical buildings. To be a bit more precise let X be a euclidean building with spherical building \(\partial X\) at infinity. Then there exists a euclidean building \(\bar{X}\) such that X splits as a product of \(\bar{X}\) with some euclidean k-space such that \(\partial \bar{X}\) is the thick reduction of \(\partial X\) in the sense of Scharlau. In addition we prove a converse statement saying that an embedding of a thick spherical building at infinity extends to an embedding of the euclidean building having the extended spherical building as its boundary.


Buildings reduction reflection subgroups thick frame 

Mathematics Subject Classification

Primary 51E24 Secondary 51D20 54E35 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Otto-von-Guericke-Universität MagdeburgMagdeburgGermany

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