TY - JOUR UR - http://lib.ugent.be/catalog/pug01:1027951 ID - pug01:1027951 LA - eng TI - Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings PY - 2010 JO - (2010) ADVANCES IN GEOMETRY SN - 1615-715X PB - 2010 AU - Struyve, Koen 002002179626 802000091679 AU - Van Maldeghem, Hendrik WE01 801000539116 0000-0002-8022-0040 AB - 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. Specializing to the discrete case of affine buildings, this solves part of a long standing conjecture about affine buildings of type (G) over tilde (2), and it reproves the results obtained mainly by the second author for types (A) over tilde (2) and (C) over tilde (2). The techniques are completely different from the ones employed in the discrete case, but they are considerably shorter, and general (i.e., independent of the type of the two-dimensional R-building). ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1027951 | ||
005 | 20180813140455.0 | ||
008 | 100823s2010------------------------eng-- | ||
022 | a 1615-715X | ||
024 | a 000279639200007 2 wos | ||
024 | a 1854/LU-1027951 2 handle | ||
024 | a 10.1515/ADVGEOM.2010.018 2 doi | ||
040 | a UGent | ||
245 | a Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings | ||
260 | c 2010 | ||
520 | a 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. Specializing to the discrete case of affine buildings, this solves part of a long standing conjecture about affine buildings of type (G) over tilde (2), and it reproves the results obtained mainly by the second author for types (A) over tilde (2) and (C) over tilde (2). The techniques are completely different from the ones employed in the discrete case, but they are considerably shorter, and general (i.e., independent of the type of the two-dimensional R-building). | ||
598 | a A1 | ||
100 | a Struyve, Koen 0 002002179626 0 802000091679 0 978197057950 | ||
700 | a Van Maldeghem, Hendrik u WE01 0 801000539116 0 0000-0002-8022-0040 | ||
650 | a Mathematics and Statistics | ||
653 | a TRIANGLE BUILDINGS | ||
653 | a QUADRANGLES | ||
653 | a valuations | ||
653 | a generalized polygons | ||
653 | a Affine buildings | ||
653 | a systems of apartments | ||
773 | t ADVANCES IN GEOMETRY g Adv. Geom. 2010. 10 (3) p.465-476 q 10:3<465 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1027951/file/1027958 z [ugent] y RBuildings3.pdf | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1027951/file/1028109 z [ugent] y Struye_2010_AG_10_3_465.pdf | ||
920 | a article | ||
852 | x WE b WE01 | ||
922 | a UGENT-WE |
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