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math.MG2009★ 1 cited
Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation
Koen Struyve, Hendrik Van Maldeghem
In this paper we complete the proof of the "equivalence" of non-discrete R-buildings of types A~_2 and C~_2, with, respectively, projective planes and generalized quadrangles with…
math.MG2009★ 1 cited
Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings
Koen Struyve, Hendrik Van Maldeghem
In this paper, we show that the building at infinity of a two-dimensional affine R-building is a generalized polygon endowed with a valuation satisfying some specific axioms. Speci…
math.MG2009★ 7 cited
(Non-)completeness of R-buildings and fixed point theorems
Koen Struyve
We prove two generalizations of results proved by Bruhat and Tits involving metrical completeness and R-buildings. Firstly, we give a generalization of the Bruhat-Tits fixed point…