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A New Axiomatics for Masures

Part of: Linear algebraic groups and related topics Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  29 January 2019

Auguste Hébert
Auguste Hébert*
Affiliation:
Université de Lyon, UJM-Saint-Etienne CNRS, UMR CNRS 5208, F-42023, Saint-Etienne, France Email: auguste.hebert@ens-lyon.fr
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Abstract

Masures are generalizations of Bruhat–Tits buildings. They were introduced by Gaussent and Rousseau to study Kac–Moody groups over ultrametric fields that generalize reductive groups. Rousseau gave an axiomatic definition of these spaces. We propose an equivalent axiomatic definition, which is shorter, more practical, and closer to the axiom of Bruhat–Tits buildings. Our main tool to prove the equivalence of the axioms is the study of the convexity properties in masures.

Keywords

MasuresHovelsKac-Moody groupsBruhat-Tits buildingslocal fields

MSC classification

Primary: 20E42: Groups with a $BN$-pair; buildings
Secondary: 20G44: Kac-Moody groups
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 3 , June 2020 , pp. 732 - 773
Copyright
© Canadian Mathematical Society 2019

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Footnotes

The author was partially supported by ANR grant ANR-15-CE40-0012.

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