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Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings

Koen Struyve and Hendrik Van Maldeghem UGent (2010) ADVANCES IN GEOMETRY. 10(3). p.465-476
abstract
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).
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
TRIANGLE BUILDINGS, QUADRANGLES, valuations, generalized polygons, Affine buildings, systems of apartments
journal title
ADVANCES IN GEOMETRY
Adv. Geom.
volume
10
issue
3
pages
465 - 476
Web of Science type
Article
Web of Science id
000279639200007
JCR category
MATHEMATICS
JCR impact factor
0.4 (2010)
JCR rank
215/276 (2010)
JCR quartile
4 (2010)
ISSN
1615-715X
DOI
10.1515/ADVGEOM.2010.018
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1027951
handle
http://hdl.handle.net/1854/LU-1027951
date created
2010-08-23 16:37:41
date last changed
2017-05-10 08:41:27
@article{1027951,
  abstract     = {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).},
  author       = {Struyve, Koen and Van Maldeghem, Hendrik},
  issn         = {1615-715X},
  journal      = {ADVANCES IN GEOMETRY},
  keyword      = {TRIANGLE BUILDINGS,QUADRANGLES,valuations,generalized polygons,Affine buildings,systems of apartments},
  language     = {eng},
  number       = {3},
  pages        = {465--476},
  title        = {Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings},
  url          = {http://dx.doi.org/10.1515/ADVGEOM.2010.018},
  volume       = {10},
  year         = {2010},
}

Chicago
Struyve, Koen, and Hendrik Van Maldeghem. 2010. “Generalized Polygons with Non-discrete Valuation Defined by Two-dimensional Affine R-buildings.” Advances in Geometry 10 (3): 465–476.
APA
Struyve, Koen, & Van Maldeghem, H. (2010). Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings. ADVANCES IN GEOMETRY, 10(3), 465–476.
Vancouver
1.
Struyve K, Van Maldeghem H. Generalized polygons with non-discrete valuation defined by two-dimensional affine R-buildings. ADVANCES IN GEOMETRY. 2010;10(3):465–76.
MLA
Struyve, Koen, and Hendrik Van Maldeghem. “Generalized Polygons with Non-discrete Valuation Defined by Two-dimensional Affine R-buildings.” ADVANCES IN GEOMETRY 10.3 (2010): 465–476. Print.