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Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation

Koen Struyve and Hendrik Van Maldeghem UGent (2011) PURE AND APPLIED MATHEMATICS QUARTERLY. 7(4). p.923-967
abstract
In this paper we complete the proof of the 'equivalence' of non-discrete R-buildings of types (A) over tilde (2) and (C) over tilde (2), with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in [7]. We also complete the proof of the 'equivalence' of an affine building of rank 3 with a generalized polygon with discrete valuation (by proving this for generalized hexagons), begun in [14]. We also complement the main result of [13] by proving uniqueness up to scalar multiples of the weight sequences of polygons with non-discrete valuation. As an application, we produce some new explicitly defined non-discrete R-buildings, in particular a class of type (A) over tilde (2) with arbitrary residues.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
affine buildings, generalized polygons, Valuation, apartment system, TRIANGLE BUILDINGS, QUADRANGLES
journal title
PURE AND APPLIED MATHEMATICS QUARTERLY
Pure Appl. Math. Q.
volume
7
issue
4
pages
923 - 967
Web of Science type
Article
Web of Science id
000287691200003
JCR category
MATHEMATICS
JCR impact factor
0.321 (2011)
JCR rank
245/288 (2011)
JCR quartile
4 (2011)
ISSN
1558-8599
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1199270
handle
http://hdl.handle.net/1854/LU-1199270
date created
2011-03-30 13:03:01
date last changed
2016-12-19 15:45:03
@article{1199270,
  abstract     = {In this paper we complete the proof of the 'equivalence' of non-discrete R-buildings of types (A) over tilde (2) and (C) over tilde (2), with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in [7]. We also complete the proof of the 'equivalence' of an affine building of rank 3 with a generalized polygon with discrete valuation (by proving this for generalized hexagons), begun in [14]. We also complement the main result of [13] by proving uniqueness up to scalar multiples of the weight sequences of polygons with non-discrete valuation. As an application, we produce some new explicitly defined non-discrete R-buildings, in particular a class of type (A) over tilde (2) with arbitrary residues.},
  author       = {Struyve, Koen and Van Maldeghem, Hendrik},
  issn         = {1558-8599},
  journal      = {PURE AND APPLIED MATHEMATICS QUARTERLY},
  keyword      = {affine buildings,generalized polygons,Valuation,apartment system,TRIANGLE BUILDINGS,QUADRANGLES},
  language     = {eng},
  number       = {4},
  pages        = {923--967},
  title        = {Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation},
  volume       = {7},
  year         = {2011},
}

Chicago
Struyve, Koen, and Hendrik Van Maldeghem. 2011. “Two-dimensional Affine R-buildings Defined by Generalized Polygons with Non-discrete Valuation.” Pure and Applied Mathematics Quarterly 7 (4): 923–967.
APA
Struyve, Koen, & Van Maldeghem, H. (2011). Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation. PURE AND APPLIED MATHEMATICS QUARTERLY, 7(4), 923–967.
Vancouver
1.
Struyve K, Van Maldeghem H. Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation. PURE AND APPLIED MATHEMATICS QUARTERLY. 2011;7(4):923–67.
MLA
Struyve, Koen, and Hendrik Van Maldeghem. “Two-dimensional Affine R-buildings Defined by Generalized Polygons with Non-discrete Valuation.” PURE AND APPLIED MATHEMATICS QUARTERLY 7.4 (2011): 923–967. Print.