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

Koen Struyve (UGent) and Hendrik Van Maldeghem (UGent)
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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.
Keywords
affine buildings, generalized polygons, Valuation, apartment system, TRIANGLE BUILDINGS, QUADRANGLES

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Citation

Please use this url to cite or link to this publication:

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.
@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},
}

Web of Science
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